Title: Relationships in Triangles
Course: quiz duplicate error

Q: Lines s, t,and u are perpendicular bisectors of [Image] and meet at J. If [Image], [Image], [Image] and [Image], find x, y,and z.
[Image]
- x = 1, y = 5, z = 5 (If s, t, and u are perpendicular bisectors, the lines coming from their circumcenter to the vertices are of equal length. Set the segments equal to each other and solve for x and y. By definition of a perpendicular bisector, [Image] so set them equal to each other and solve.)
- x = 2.5, y = 2, z = 2.3 (If s, t, and u are perpendicular bisectors, the lines coming from their circumcenter to the vertices are of equal length. Set the segments equal to each other and solve for x and y. By definition of a perpendicular bisector, [Image] so set them equal to each other and solve.)
- x = 5, y = 1, z = 5 (If s, t, and u are perpendicular bisectors, the lines coming from their circumcenter to the vertices are of equal length. Set the segments equal to each other and solve for x and y. By definition of a perpendicular bisector, [Image] so set them equal to each other and solve.)
- x = 0, y = 6, z = 2.3 (If s, t, and u are perpendicular bisectors, the lines coming from their circumcenter to the vertices are of equal length. Set the segments equal to each other and solve for x and y. By definition of a perpendicular bisector, [Image] so set them equal to each other and solve.)
A: x = 1, y = 5, z = 5

Q: [Image]is an angle bisector. [Image], [Image], and [Image]. Find [Image]. Is [Image]?
[Image]
- 63; No (If RU is an angle bisector, the two angles of vertex R are equal. Also, the measures of the angles of every triangle add up to 180.)
- 65; No (If RU is an angle bisector, the two angles of vertex R are equal. Also, the measures of the angles of every triangle add up to 180.)
- 60; Yes (If RU is an angle bisector, the two angles of vertex R are equal. Also, the measures of the angles of every triangle add up to 180.)
- 29; No (If RU is an angle bisector, the two angles of vertex R are equal. Also, the measures of the angles of every triangle add up to 180.)
A: 63; No

Q: [Image]is an angle bisector. [Image], [Image], and [Image]. Find [Image].
[Image]
- 40 (If [Image] is an angle bisector, the two angles of vertex X are equal. Also, the measures of the angles of every triangle add up to 180.)
- 35 (If [Image] is an angle bisector, the two angles of vertex X are equal. Also, the measures of the angles of every triangle add up to 180.)
- 38 (If [Image] is an angle bisector, the two angles of vertex X are equal. Also, the measures of the angles of every triangle add up to 180.)
- 30 (If [Image] is an angle bisector, the two angles of vertex X are equal. Also, the measures of the angles of every triangle add up to 180.)
A: 38

Q: [Image]is an altitude. [Image], [Image]. Find [Image].
[Image]
- 34 (If [Image] is an altitude, [Image]. Also, the measures of the angles of every triangle add up to 180.)
- 32 (If [Image] is an altitude, [Image]. Also, the measures of the angles of every triangle add up to 180.)
- 18 (If [Image] is an altitude, [Image]. Also, the measures of the angles of every triangle add up to 180.)
- 31 (If [Image] is an altitude, [Image]. Also, the measures of the angles of every triangle add up to 180.)
A: 34

Q: [Image]is an angle bisector. [Image], [Image], [Image]. Find [Image]. Is [Image] an altitude?
[Image]
- 45; Yes (The measures of the angles of every triangle add up to 180. If [Image] is an altitude, [Image].)
- 48; No (The measures of the angles of every triangle add up to 180. If [Image] is an altitude, [Image].)
- 32; No (The measures of the angles of every triangle add up to 180. If [Image] is an altitude, [Image].)
- 52; No (The measures of the angles of every triangle add up to 180. If [Image] is an altitude, [Image].)
A: 48; No

Q: Determine the relationship between the measures of the given angles.

[Image]
[Image]
- [Image] (The measures of the sides opposite the angles given are compared. The longer the side, the larger its angle.)
- [Image] (The measures of the sides opposite the angles given are compared. The longer the side, the larger its angle.)
- [Image] (The measures of the sides opposite the angles given are compared. The longer the side, the larger its angle.)
A: [Image]

Q: Determine the relationship between the measures of the given angles.

[Image]
[Image]
- [Image] (Different names for the same angle.)
- [Image] (Different names for the same angle.)
- [Image] (Different names for the same angle.)
A: [Image]

Q: Determine the relationship between the lengths of the given sides.

[Image]
[Image]
- [Image] (The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side.)
- [Image] (The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side.)
- cannot be determined (The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side.)
- [Image] (The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side.)
A: cannot be determined

Q: Determine the relationship between the lengths of the given sides.

[Image]
[Image]
- [Image] (The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side.)
- [Image] (The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side.)
- [Image] (The measures of the angles opposite the sides given are compared. The larger the angle, the longer its side.)
A: [Image]

Q: Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.

3, 9, 10
- Yes; the third side is the longest. (The sum of the lengths of any two sides must be greater than the third.)
- No; the sum of the lengths of two sides is not greater than the third. (The sum of the lengths of any two sides must be greater than the third.)
- No; the first side is not long enough. (The sum of the lengths of any two sides must be greater than the third.)
- Yes; the sum of the lengths of any two sides is greater than the third. (The sum of the lengths of any two sides must be greater than the third.)
A: Yes; the sum of the lengths of any two sides is greater than the third.

Q: Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. Explain.

9.2, 14.5, 17.1
- Yes; the third side is the longest. (The sum of the lengths of any two sides must be greater than the third.)
- No; the first side is not long enough. (The sum of the lengths of any two sides must be greater than the third.)
- Yes; the sum of the lengths of any two sides is greater than the third. (The sum of the lengths of any two sides must be greater than the third.)
- No; the sum of the lengths of two sides is not greater than the third. (The sum of the lengths of any two sides must be greater than the third.)
A: Yes; the sum of the lengths of any two sides is greater than the third.

Q: An isosceles triangle has a base 9.6 units long. If the congruent side lengths have measures to the first decimal place, what is the shortest possible length of the sides?
- 4.9 (The sum of the lengths of any two sides must be greater than the third.)
- 19.3 (The sum of the lengths of any two sides must be greater than the third.)
- 4.7 (The sum of the lengths of any two sides must be greater than the third.)
- 9.7 (The sum of the lengths of any two sides must be greater than the third.)
A: 4.9

Q: Which segment is the shortest possible distance from point D to plane P?
[Image]
- [Image] (The shortest possible distance from point D to plane P is a straight line perpendicular to plane P through point D.)
- [Image] (The shortest possible distance from point D to plane P is a straight line perpendicular to plane P through point D.)
- [Image] (The shortest possible distance from point D to plane P is a straight line perpendicular to plane P through point D.)
- [Image] (The shortest possible distance from point D to plane P is a straight line perpendicular to plane P through point D.)
A: [Image]

Write a two-column proof.

If [Image] and [Image], then [Image].
[Image]

Write a two-column proof.

If [Image] is a median of isosceles [Image], then [Image].
[Image]

Write a two-column proof.

If [Image] is a median and a perpendicular bisector of [Image], then [Image].
[Image]

Write a two-column proof.

Given: [Image]
Prove: [Image]
[Image]

Write a two-column proof.

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

Write a two-column proof.

Given: [Image], [Image]
Prove: [Image]
[Image]

Write an indirect proof.

Given: [Image]
Prove: [Image]

Write an indirect proof.

Given: [Image]
Prove: [Image] is positive

Write an indirect proof.

If [Image] and [Image], then [Image].

Write an indirect proof.

If n is a multiple of 9 then it is a multiple of 3.

Write an indirect proof.

If [Image] then [Image].

Write an indirect proof.

If [Image] is an integer, then n is even.

Write an indirect proof.

Given: [Image] is an even number
Prove: n is an even number

Write an indirect proof.

Given: [Image], [Image]
Prove: [Image]
[Image]

Write an indirect proof.

Given: [Image]
Prove: [Image]
[Image] [Image]

Write an indirect proof.

Given: A is the midpoint of BF and CD.
Prove: [Image]
[Image]

Write an indirect proof.

Given: [Image] is a perpendicular bisector of equilateral triangle [Image].
Prove: [Image]
[Image]

Write an indirect proof.

Given: [Image] is a perpendicular bisector of equilateral triangle [Image]. [Image] is a median of [Image].
Prove: [Image]
[Image]

Write an indirect proof.

Given: Square GHJK
Prove: [Image]
[Image]

Write an indirect proof.

Given: [Image] with angle measures as shown.
Prove: [Image]
[Image]

Write an indirect proof.

Given: [Image] is a perpendicular bisector of [Image].
Prove: [Image] is isosceles
[Image]

Write an indirect proof.

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

The vertices of a triangle are [Image].
a.      Graph the triangle.
b.      Use the Distance Formula to find the length of each side to the nearest tenth.
c.      [Image] is a median of the triangle. What are the coordinates of point O? Explain.
d.      Graph median [Image].

Greg baby-sits his two neighbors after school three days per week. He is paid $15 per day.
a.      Graph the amount of money that Greg accumulates for babysitting.
b.      Use the slope of the line to write an argument that the line intersects the $120 line at [Image].
c.      What does the point [Image] represent?
d.      Greg is saving for a $360 electric scooter. Use the slope of the line to find out how many weeks it will take him to save this much. Show your work.

Q: Determine the relationship between the lengths of the given sides.

[Image]
[Image]
- [Image] (You can only compare sides that are part of the same triangle.)
- [Image] (You can only compare sides that are part of the same triangle.)
- cannot be determined (You can only compare sides that are part of the same triangle.)
- [Image] (You can only compare sides that are part of the same triangle.)
A: cannot be determined