Title: Proportions and Similarity
Course: quiz duplicate error

Q: At Whitewater Junior High School, there are 360 students and 39 teachers. What is the ratio of students to each teacher rounded to the nearest tenth?
- 1:9.2 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
- 9.2:1 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
- 120:13 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
- 13:120 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
A: 9.2:1

Q: During the past school year, there were 640 students and 52 teachers. What is the ratio of students to each teacher rounded to the nearest tenth?
- 12.3:1 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
- 1:12.3 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
- 160:13 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
- 13:160 (To find this ratio, divide the number of students by the number of teachers. Round your answer to the nearest tenth.)
A: 12.3:1

Q: Find x and the measures of the indicated parts.

[Image]
AB and BC
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
A: [Image]

Q: There are 84 boys in a freshman class of 146 students. Find the ratio of boys to girls.
- 42:73 (How many boys are in the freshman class? Subtract the number of boys from the class population to determine the number of girls in the class. Simplify the ratio.)
- 31:42 (How many boys are in the freshman class? Subtract the number of boys from the class population to determine the number of girls in the class. Simplify the ratio.)
- 42:31 (How many boys are in the freshman class? Subtract the number of boys from the class population to determine the number of girls in the class. Simplify the ratio.)
- 73:42 (How many boys are in the freshman class? Subtract the number of boys from the class population to determine the number of girls in the class. Simplify the ratio.)
A: 42:31

Q: Identify the similar triangles. Find x.

[Image] [Image]
- [Image]; [Image] ([Image])
- [Image]; [Image] ([Image])
- [Image]; [Image] ([Image])
- [Image]; [Image] ([Image])
A: [Image]; [Image]

Q: Determine whether each pair of triangles is similar. Justify your answer.

[Image]
- yes; [Image] by AA Similarity ([Image] so [Image].)
- yes; [Image] by AA Similarity ([Image] so [Image].)
- yes; [Image] by ASA Similarity ([Image] so [Image].)
- No; there is not enough information to determine similarity. ([Image] so [Image].)
A: yes; [Image] by AA Similarity

Q: Identify the similar triangles. Find x.

[Image] [Image]
- [Image]; [Image] (The ratio of corresponding sides is 2:3. [Image])
- [Image]; [Image] (The ratio of corresponding sides is 2:3. [Image])
- [Image]; [Image] (The ratio of corresponding sides is 2:3. [Image])
- [Image]; [Image] (The ratio of corresponding sides is 2:3. [Image])
A: [Image]; [Image]

Q: A basketball player made 36 free throws in 16 games. Find the ratio of free throws to games.
- 4:9 (How many free throws were scored? How many games are played? The ratio should be written in simplest form.)
- 9:4 (How many free throws were scored? How many games are played? The ratio should be written in simplest form.)
- 6:4 (How many free throws were scored? How many games are played? The ratio should be written in simplest form.)
- 9:5 (How many free throws were scored? How many games are played? The ratio should be written in simplest form.)
A: 9:4

Q: There are 96 girls in a junior class of 176 students. Find the ratio of girls to boys.
- 11:6 (How many girls are in the junior class? Subtract the number of girls from the class population to determine the number of boys in the class. Simplify the ratio.)
- 5:6 (How many girls are in the junior class? Subtract the number of girls from the class population to determine the number of boys in the class. Simplify the ratio.)
- 6:11 (How many girls are in the junior class? Subtract the number of girls from the class population to determine the number of boys in the class. Simplify the ratio.)
- 6:5 (How many girls are in the junior class? Subtract the number of girls from the class population to determine the number of boys in the class. Simplify the ratio.)
A: 6:5

Q: A hockey player made 9 goals in 12 games. Find the ratio of goals to games.
- 3:4 (How many goals are scored? How many games are played? Simplify the results.)
- 4:3 (How many goals are scored? How many games are played? Simplify the results.)
- 1:3 (How many goals are scored? How many games are played? Simplify the results.)
- 3:1 (How many goals are scored? How many games are played? Simplify the results.)
A: 3:4

Q: Solve each proportion.

[Image]
- [Image] (Find the cross products. Multiply. Divide each side by the coefficient of the variable.)
- [Image] (Find the cross products. Multiply. Divide each side by the coefficient of the variable.)
- [Image] (Find the cross products. Multiply. Divide each side by the coefficient of the variable.)
- [Image] (Find the cross products. Multiply. Divide each side by the coefficient of the variable.)
A: [Image]

Q: Determine whether each pair of triangles is similar. Justify your answer.

[Image] [Image]
- No; sides are not proportional. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. The ratio of the corresponding sides is 1:3.)
- yes; [Image] by SSS Similarity (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. The ratio of the corresponding sides is 1:3.)
- yes; [Image] by SSS Similarity (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. The ratio of the corresponding sides is 1:3.)
- yes; [Image] by SSS Similarity (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional. The ratio of the corresponding sides is 1:3.)
A: yes; [Image] by SSS Similarity

Q: For a recent project, a teacher purchased 250 pieces of red construction paper and 114 pieces of blue construction paper. What is the ratio of red to blue?
- 57:125 (Find the number of pieces of red construction paper. Find the number of pieces of blue construction paper. Simplify the ratio.)
- 125:57 (Find the number of pieces of red construction paper. Find the number of pieces of blue construction paper. Simplify the ratio.)
- 125:182 (Find the number of pieces of red construction paper. Find the number of pieces of blue construction paper. Simplify the ratio.)
- 182:125 (Find the number of pieces of red construction paper. Find the number of pieces of blue construction paper. Simplify the ratio.)
A: 125:57

Q: Find x and the measures of the indicated parts.

[Image]
AB
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
A: [Image]

Q: Each pair of polygons is similar. Write a similarity statement, and find x, the measures of the indicated sides, and the scale factor.

[Image] and [Image]
[Image] [Image]
- [Image]; [Image]; [Image]; 3.6 (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
- [Image]; [Image]; [Image]; [Image] (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
- [Image]; [Image]; [Image]; [Image]; 3.6 (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
- [Image]; [Image]; [Image]; [Image]; 3.6 (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
A: [Image]; [Image]; [Image]; [Image]; 3.6

Q: Determine whether each pair of figures is similar. Justify your answer.

[Image] [Image]
- [Image] is not similar to [Image]. Corresponding angles are not the same. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
- [Image] because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 1. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
- [Image] is not similar to [Image]. The ratios of the corresponding sides are not the same. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
- [Image] because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 2. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
A: [Image] because the corresponding angles of each triangle are congruent. The ratio of the corresponding sides is 1.

Q: Each pair of polygons is similar. Write a similarity statement, and find x, the measures of the indicated sides, and the scale factor.

[Image] and [Image]
[Image] [Image]
- [Image]; [Image]; [Image]; [Image] (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
- [Image]; [Image]; [Image]; 3.8 (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
- [Image]; [Image]; [Image]; [Image]; 3.8 (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
- [Image]; [Image]; [Image]; [Image]; 3.8 (Use the congruent angles to write the corresponding vertices in order. Write proportions to find the missing information.)
A: [Image]; [Image]; [Image]; [Image]; 3.8

Q: Use the number line below to determine the ratio of BC to GK.
[Image]
- 5:1 (Find the length of BC. Then find the length of GK. Write the ratio in simplest form.)
- 4:1 (Find the length of BC. Then find the length of GK. Write the ratio in simplest form.)
- 1:5 (Find the length of BC. Then find the length of GK. Write the ratio in simplest form.)
- 1:4 (Find the length of BC. Then find the length of GK. Write the ratio in simplest form.)
A: 1:4

Q: Use the number line below to determine the ratio of AD to EI.
[Image]
- 3:8 (Find the length of AD. Then find the length of EI. Write the ratio in simplest form.)
- 4:3 (Find the length of AD. Then find the length of EI. Write the ratio in simplest form.)
- 3:4 (Find the length of AD. Then find the length of EI. Write the ratio in simplest form.)
- 8:3 (Find the length of AD. Then find the length of EI. Write the ratio in simplest form.)
A: 3:4

Q: A baseball player made six hits in nine innings. What is the ratio of hits to innings?
- 2:3 (How many hits does the player have? How many innings did the player play? Simplify the ratio.)
- 3:2 (How many hits does the player have? How many innings did the player play? Simplify the ratio.)
- 2:5 (How many hits does the player have? How many innings did the player play? Simplify the ratio.)
- 5:2 (How many hits does the player have? How many innings did the player play? Simplify the ratio.)
A: 2:3

Q: Determine whether each pair of triangles is similar. Justify your answer.

[Image]
- No; the sides are not congruent. ([Image] so [Image].)
- yes; [Image] by SSS Similarity ([Image] so [Image].)
- yes; [Image] by ASA Similarity ([Image] so [Image].)
- yes; [Image] by SAS Similarity ([Image] so [Image].)
A: yes; [Image] by SAS Similarity

Q: Determine whether each pair of figures is similar. Justify your answer.

[Image] [Image]
- [Image] is not similar to [Image] because the ratio of the corresponding sides is proportional. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
- [Image] is not similar to [Image] because the corresponding angles are not congruent. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
- [Image] because the ratio of the corresponding sides is proportional and the corresponding angles are congruent. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
- [Image] is not similar to [Image] because the ratio of the corresponding sides is not proportional. (Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.)
A: [Image] is not similar to [Image] because the corresponding angles are not congruent.

Q: Find x and the measures of the indicated parts.

[Image]
BC and AC
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
A: [Image]

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], given [Image], [Image], [Image], and [Image].
[Image]
- 28.3 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 8.3 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 5 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 13.3 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 28.3

Q: Find AD if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 30 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 40 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 10 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 8 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 30

Q: Find AD if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 15 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 48 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 6 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 18 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 18

Q: Determine whether [Image]. Justify your answer.
[Image]
[Image], [Image], [Image], [Image]
- no, [Image] [Image] (Determine the ratio for both sides of the triangle. If the ratios are congruent, then the segments are parallel.)
- yes, [Image] [Image], [Image] [Image] (Determine the ratio for both sides of the triangle. If the ratios are congruent, then the segments are parallel.)
- yes, [Image] [Image] (Determine the ratio for both sides of the triangle. If the ratios are congruent, then the segments are parallel.)
- no, [Image] [Image], [Image] [Image] (Determine the ratio for both sides of the triangle. If the ratios are congruent, then the segments are parallel.)
A: yes, [Image] [Image]

Q: Find XZ if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 18 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 12 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 27 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 9 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 27

Q: Find x so that [Image].
[Image]
[Image], [Image], [Image], [Image]
- 6.38 (Create a proportion using the Triangle Proportionality Theorem. Cross multiply. Solve for the variable.)
- 21 (Create a proportion using the Triangle Proportionality Theorem. Cross multiply. Solve for the variable.)
- 24 (Create a proportion using the Triangle Proportionality Theorem. Cross multiply. Solve for the variable.)
- 9.38 (Create a proportion using the Triangle Proportionality Theorem. Cross multiply. Solve for the variable.)
A: 21

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], given [Image], [Image], [Image], and [Image].
[Image]
- 11.25 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 21.25 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 47.5 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 38 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 47.5

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], perimeter of [Image], [Image], and [Image].
[Image]
- 20 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 101.25 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 45 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 90 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 101.25

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], given [Image], [Image], and [Image].
[Image]
- 45 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 28.8 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 48 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 72 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 45

Q: Find x and the measures of the indicated parts.

[Image] | [Image]

BD and CE
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
A: [Image]

Q: Find XZ if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 3 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 2 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 9 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 4 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 9

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], perimeter of [Image], [Image], and [Image].
[Image]
- 112 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 64 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 56 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 49 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 49

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], [Image] is a parallelogram, [Image], [Image], [Image], and [Image].
[Image]
- 32 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 56 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 24 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 13.7 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 32

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], given [Image], [Image], [Image], and [Image].
[Image]
- 72 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 16 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 14 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 48 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 48

Q: Find x and the measures of the indicated parts.

[Image]
AS
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
A: [Image]

Q: Find BD if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 8 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 14 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 10 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 2 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 14

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], given [Image], [Image], and [Image].
[Image]
- 48 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 32 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 40 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 80 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 32

Q: Find the length of [Image] if [Image] and [Image] is a midsegment of [Image].
[Image]
- 12.25 (A midsegment of a triangle is one-half the length of the third side.)
- [Image] (A midsegment of a triangle is one-half the length of the third side.)
- 49 (A midsegment of a triangle is one-half the length of the third side.)
- [Image] (A midsegment of a triangle is one-half the length of the third side.)
A: [Image]

Q: Find WZ if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 21 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 15 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 3 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 7 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 15

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], given [Image], [Image], [Image], and [Image].
[Image]
- 28 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 14 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 10 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 5.5 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 14

Q: Find x and the measures of the indicated parts.

[Image]
AB and AC
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
A: [Image]

Q: Find the perimeter of the given triangle. Round your answer to the nearest tenth if necessary.

[Image], if [Image], given [Image], [Image], and [Image].
[Image]
- 120 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 60 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 156 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
- 23.1 (Use the Proportional Perimeter Theorem to find the perimeter of the selected triangle.)
A: 156

Q: Find WZ if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 16 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 9 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 20 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 4 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 16

Q: Find x and the measures of the indicated parts.

[Image]
EB and ED
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
- [Image] (Determine the ratio of corresponding parts. Use the ratio to find the missing information.)
A: [Image]

Q: Find the length of [Image] if [Image] and [Image] is a midsegment of [Image].
[Image]
- [Image] (A midsegment of a triangle is one-half the length of the third side.)
- 49 (A midsegment of a triangle is one-half the length of the third side.)
- 12.25 (A midsegment of a triangle is one-half the length of the third side.)
- [Image] (A midsegment of a triangle is one-half the length of the third side.)
A: [Image]

Q: What is the sum of the numbers in the tenth row of Pascal’s Triangle?
- 512 ([Image])
- 513 ([Image])
- 1,023 ([Image])
- 1,024 ([Image])
A: 512

Generate seven rows of Pascal’s Triangle.

Write a two-column proof.

Given: [Image] bisects [Image]. [Image]
Prove: [Image]
[Image]

Determine whether each pair of triangles is similar. Justify your answer.

[Image]

In [Image], [Image] is equidistant from [Image].

a.      Draw a picture to represent the situation.
b.      Suppose [Image] ft, [Image] ft, [Image] ft. What is the length of [Image]?

Q: Find the first three iterates of each expression.

[Image], m initially equals 1
- 13, 8, 5 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
- 5, 8, 13 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
- 5, 29, 845 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
- 845, 29, 5 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
A: 5, 29, 845

A cell phone company charges a one-time installation fee and a monthly flat rate as shown in the graph.

[Image] | [Image]

a.      What is the slope of the line that joins the points on the graph?
b.      What does the value of the slope represent?
c.      Write the equation of the line.

Q: What is the sum of the numbers in the fourth row of Pascal’s Triangle?
- 4 ([Image])
- 6 ([Image])
- 7 ([Image])
- 8 ([Image])
A: 8

Write the indicated type of proof.

Given: [Image] bisects [Image]. [Image], [Image]
Prove: [Image]
[Image]

Q: Find the sum of the first 35 numbers in the outside diagonal of Pascal’s Triangle.
- 34 (The outside diagonal of Pascal’s Triangle contains 35 ones. The sum would be 35.)
- 35 (The outside diagonal of Pascal’s Triangle contains 35 ones. The sum would be 35.)
- 36 (The outside diagonal of Pascal’s Triangle contains 35 ones. The sum would be 35.)
- 37 (The outside diagonal of Pascal’s Triangle contains 35 ones. The sum would be 35.)
A: 35

[Image]

Q: Find the first three iterates of each expression.

[Image], s initially equals 2
- –16, –11, –6 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
- –166, 34, –6 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
- –6, 34, –166 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
- –6, –11, –16 (Find the value of the first iterate. Then use that value to find the next iterate in the expression. Repeat to find the third iterate.)
A: –6, 34, –166

Q: What is the sum of the numbers in the eighth row of Pascal’s Triangle?
- 8 ([Image])
- 126 ([Image])
- 128 ([Image])
- 256 ([Image])
A: 128

Q: Count the number of dots in each arrangement. How many dots will be in the sixth triangular number?
[Image]
- 6 (In the sixth triangular number, the bottom row will contain six dots. The row above the bottom row will contain five dots. This continues until the top row contains one dot. The total number of dots is 21.)
- 15 (In the sixth triangular number, the bottom row will contain six dots. The row above the bottom row will contain five dots. This continues until the top row contains one dot. The total number of dots is 21.)
- 21 (In the sixth triangular number, the bottom row will contain six dots. The row above the bottom row will contain five dots. This continues until the top row contains one dot. The total number of dots is 21.)
- 28 (In the sixth triangular number, the bottom row will contain six dots. The row above the bottom row will contain five dots. This continues until the top row contains one dot. The total number of dots is 21.)
A: 21

Q: Count the number of dots in each arrangement. How many dots will be in the sixth arrangement?

•
••
••
•••
•••
•••
••••
••••
••••
••••
- 36 (Each arrangement is the square of the iterate. Therefore, the sixth iterate would be [Image])
- 25 (Each arrangement is the square of the iterate. Therefore, the sixth iterate would be [Image])
- 16 (Each arrangement is the square of the iterate. Therefore, the sixth iterate would be [Image])
- 30 (Each arrangement is the square of the iterate. Therefore, the sixth iterate would be [Image])
A: 36

Q: What is the sum of the first 50 numbers in the outside diagonal of Pascal’s Triangle?
- 49 (The outside diagonal of Pascal’s Triangle contains 50 one’s. The sum would be 50.)
- 50 (The outside diagonal of Pascal’s Triangle contains 50 one’s. The sum would be 50.)
- 51 (The outside diagonal of Pascal’s Triangle contains 50 one’s. The sum would be 50.)
- 52 (The outside diagonal of Pascal’s Triangle contains 50 one’s. The sum would be 50.)
A: 50

Q: Find WZ if [Image], [Image] and [Image] are medians, [Image], [Image], [Image], and [Image].
[Image] [Image]
- 3 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 45 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 5 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
- 20 (Write a proportion. Substitute the given values for the sides. Cross multiply, and simplify.)
A: 20

Q: Count the number of dots in each arrangement. How many dots will be in the fifth arrangement?

•• | •• •• | •• •• ••
- 8 (Each arrangement increases by two dots every time. The fifth arrangement will contain ten dots.)
- 10 (Each arrangement increases by two dots every time. The fifth arrangement will contain ten dots.)
- 12 (Each arrangement increases by two dots every time. The fifth arrangement will contain ten dots.)
- 50 (Each arrangement increases by two dots every time. The fifth arrangement will contain ten dots.)
A: 10

Q: Find the sum of the first 18 numbers in the outside diagonal of Pascal’s Triangle.
- 17 (The outside diagonal of Pascal’s Triangle contains 18 ones. The sum would be 18.)
- 18 (The outside diagonal of Pascal’s Triangle contains 18 ones. The sum would be 18.)
- 19 (The outside diagonal of Pascal’s Triangle contains 18 ones. The sum would be 18.)
- 20 (The outside diagonal of Pascal’s Triangle contains 18 ones. The sum would be 18.)
A: 18