Title: Congruent Triangles
Course: quiz duplicate error

Q: Find each measure.

[Image]
[Image]
- [Image] (The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.)
- [Image] (The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.)
- [Image] (The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.)
- [Image] (The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.)
A: [Image]

Q: Identify the congruent triangles in the figure.

[Image]
- [Image] (The letters naming the triangles correspond to the congruent vertices of the two triangles in the same order.)
- [Image] (The letters naming the triangles correspond to the congruent vertices of the two triangles in the same order.)
- [Image] (The letters naming the triangles correspond to the congruent vertices of the two triangles in the same order.)
- [Image] (The letters naming the triangles correspond to the congruent vertices of the two triangles in the same order.)
A: [Image]

Q: Find each measure.

[Image]
[Image]
- [Image] (The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.)
- [Image] (The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.)
- [Image] (The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.)
- [Image] (The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.)
A: [Image]

Q: Use a protractor to classify the triangle as acute, equiangular, obtuse, or right.

[Image]
- right (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle. An equiangular triangle has at least 2 congruent sides.)
- acute (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle. An equiangular triangle has at least 2 congruent sides.)
- equiangular (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle. An equiangular triangle has at least 2 congruent sides.)
- obtuse (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle. An equiangular triangle has at least 2 congruent sides.)
A: acute

Q: Determine whether [Image] given the coordinates of the vertices. Explain.

[Image]
- Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; each side of triangle PQR is not the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; neither side has a right angle. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- Yes; two sides of triangle PQR and angle PQR are the same measure as the corresponding sides and angle of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
A: No; each side of triangle PQR is not the same length as the corresponding side of triangle STU.

Q: Determine whether [Image] given the coordinates of the vertices. Explain.

[Image]
- No; each side of triangle PQR is not the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- Yes; both triangles have an obtuse angle. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
A: Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU.

Q: Determine whether [Image] given the coordinates of the vertices. Explain.

[Image]
- Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; each side of triangle PQR is not the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- Yes; both triangles have three sides. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
A: Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU.

Q: Determine whether [Image] given the coordinates of the vertices. Explain.

[Image]
- Yes; both triangles have three acute angles. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; each side of triangle PQR is not the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
A: Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU.

Q: Use a protractor to classify the triangle as acute, equiangular, obtuse, or right.

[Image]
- equiangular (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle.)
- obtuse (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle.)
- acute (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle.)
- right (An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle.)
A: equiangular

Q: Find the measures of the sides of [Image] and classify the triangle by its sides.

[Image]
- equilateral (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
- obtuse (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
- isosceles (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
- scalene (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
A: scalene

Q: Name the congruent angles and sides for the pair of congruent triangles.

[Image]
- [Image] [Image] (The corresponding sides and angles can be determined from any congruence statement by following the order of the letters.)
- [Image] [Image] (The corresponding sides and angles can be determined from any congruence statement by following the order of the letters.)
- [Image] [Image] (The corresponding sides and angles can be determined from any congruence statement by following the order of the letters.)
- [Image] [Image] (The corresponding sides and angles can be determined from any congruence statement by following the order of the letters.)
A: [Image] [Image]

Q: Find the measures of the sides of [Image] and classify the triangle by its sides.

[Image]
- equilateral (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
- isosceles (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
- scalene (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
- obtuse (Use the Distance Formula to find the lengths of the sides. [Image] If [Image] or [Image] or [Image], then the triangle is isosceles. If [Image], then the triangle is equilateral. If neither of the above, the triangle is scalene.)
A: scalene

Q: Triangle RSU is an equilateral triangle. [Image] bisects [Image]. Find x and y.
[Image]
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
A: [Image]

Q: Position and label the triangle on the coordinate plane.

isosceles [Image] with base [Image] 2b units long
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Q: Triangle FJH is an equilateral triangle. Find x and y.
[Image]
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
A: [Image]

Q: Triangles ABC and AFD are vertical congruent equilateral triangles. Find x and y.
[Image]
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
A: [Image]

Q: Position and label the triangle on the coordinate plane.

right [Image] with non-hypotenuse side [Image] twice as long as non-hypotenuse side [Image]. [Image] is a units long
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Q: Position and label the triangle on the coordinate plane.

equilateral [Image] with height a units and one-half base [Image]b units
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Q: Position and label the triangle on the coordinate plane.

right [Image] with hypotenuse [Image], leg [Image] 4a units long, and leg [Image] one-fourth the other leg
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

What is [Image]?
- 74 (Add [Image].)
- 68 (Add [Image].)
- 64 (Add [Image].)
- 78 (Add [Image].)
A: 74

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

What is [Image]?
- 118 ([Image].)
- 114 ([Image].)
- 112 ([Image].)
- 104 ([Image].)
A: 104

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

If [Image] what is [Image]?
- 96 ([Image]. [Image].)
- 124 ([Image]. [Image].)
- 132 ([Image]. [Image].)
- 138 ([Image]. [Image].)
A: 132

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

If [Image] what is [Image]?
- 96 ([Image]. [Image].)
- 134 ([Image]. [Image].)
- 152 ([Image]. [Image].)
- 138 ([Image]. [Image].)
A: 134

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

If [Image] what is [Image]?
- 45 ([Image].)
- 55 ([Image].)
- 65 ([Image].)
- 35 ([Image].)
A: 45

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

If [Image], what is [Image]?
- 24 ([Image])
- 16 ([Image])
- 12 ([Image])
- 18 ([Image])
A: 24

Q: Triangles MNP and OMN are congruent equilateral triangles. Find x and y.
[Image]
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
- [Image] ([Image] [Image])
A: [Image]

Q: Position and label the triangle on the coordinate plane.

right isosceles [Image] with congruent sides [Image] and [Image]a units long
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

If [Image] what is [Image]?
- 98 ([Image].)
- 95 ([Image].)
- 23 ([Image].)
- 94 ([Image].)
A: 95

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

What is [Image]?
- 23 (Since [Image] is isosceles, [Image].)
- 38 (Since [Image] is isosceles, [Image].)
- 42 (Since [Image] is isosceles, [Image].)
- 35 (Since [Image] is isosceles, [Image].)
A: 38

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

What is [Image]?
- 80 (Since [Image] is isosceles, [Image].)
- 38 (Since [Image] is isosceles, [Image].)
- 64 (Since [Image] is isosceles, [Image].)
- 72 (Since [Image] is isosceles, [Image].)
A: 72

Q: Refer to the figure. [Image] are all isosceles triangles.
[Image]

What is [Image]?
- 16 (Since [Image] is isosceles, [Image]. Subtract those from 180 to get the answer.)
- 38 (Since [Image] is isosceles, [Image]. Subtract those from 180 to get the answer.)
- 36 (Since [Image] is isosceles, [Image]. Subtract those from 180 to get the answer.)
- 108 (Since [Image] is isosceles, [Image]. Subtract those from 180 to get the answer.)
A: 36

Q: Determine whether [Image] given the coordinates of the vertices. Explain.

[Image]
- Yes; two sides of triangle PQR and angle PQR are the same measure as the corresponding sides and angle of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- Yes; each side of triangle PQR is the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; one of the triangles is obtuse. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
- No; each side of triangle PQR is not the same length as the corresponding side of triangle STU. (If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent.)
A: No; each side of triangle PQR is not the same length as the corresponding side of triangle STU.

Write a flow proof.

Given: M is the midpoint of [Image]. [Image], [Image], [Image]
Prove: [Image]
[Image]

Write a two-column proof.

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

Write a coordinate proof for the statement.

The three segments joining the midpoints of the sides of an isosceles triangle form another isosceles triangle.

Write a paragraph proof.

Given: Vertical isosceles triangles. [Image] bisects [Image]. [Image].
Prove: [Image]
[Image]

Write a two-column proof.

Given: P is the midpoint of [Image]. [Image].
Prove: [Image]
[Image]

Write a two-column proof.

Given: Circle Q. [Image] are isosceles. [Image]and [Image] are vertex angles. [Image]. [Image].
Prove: [Image]
[Image]

Q: Position and label the triangle on the coordinate plane.

one-half equilateral triangle with [Image] bisecting the triangle at height a units and base [Image] 2b units
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Write a coordinate proof for the statement.

The three segments joining the midpoints of the sides of an equilateral triangle form another equilateral triangle.

Q: Position and label the triangle on the coordinate plane.

isosceles [Image] with [Image] twice the length of the base and bisecting the base
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Write a two-column proof.

Given: W is the midpoint of [Image] and [Image]. [Image].
Prove: [Image]
[Image]

Q: Position and label the triangle on the coordinate plane.

equilateral [Image] with height c units and base [Image] 2d units
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Write a two-column proof.

Given: [Image] is isosceles. [Image]. [Image]. [Image].
Prove: [Image]
[Image]

Write a two-column proof.

Given: A trapezoid. [Image]. [Image]. [Image] perpendicular to [Image] and [Image]. [Image] perpendicular to [Image] and [Image].
Prove: [Image]
[Image]

Write a coordinate proof for the statement.

If a segment is drawn to connect the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side.

Write a two-column proof.

Given: R is the midpoint of [Image], [Image].
Prove: [Image]
[Image]

Write a two-column proof.

Given: [Image] is isosceles. [Image]. [Image].
Prove: [Image]
[Image]

Write a coordinate proof for the statement.

The segment that joins the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base.

Write a flow proof.

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

Write a coordinate proof for the statement.

A triangle with coordinates [Image], [Image], [Image] is isosceles.

Write a coordinate proof for the statement.

If a line is drawn between the midpoints of two sides of a triangle, then the line is parallel to the third side.

Write a two-column proof.

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

Write a two-column proof.

Given: [Image] is equilateral. [Image] bisects [Image].
Prove: T is the midpoint of [Image].
[Image]

Write a flow proof.

Given: Rectangle ZYWX. [Image].
Prove: [Image]
[Image]

Write a flow proof.

Given: Square ABCD. [Image].
Prove: [Image]
[Image]

Write a coordinate proof for the statement.

If a line is drawn between the midpoints of two sides of an equiangular triangle, then the resulting triangle is also equiangular.

Q: Position and label the triangle on the coordinate plane.

isosceles [Image] with [Image] half the length of the base and bisecting the base
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Write a two-column proof.

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

Write a coordinate proof for the statement.

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Write a paragraph proof.

Given: Square VWXY. [Image].
Prove: [Image]
[Image]

Write a flow proof.

Given: Two interlocked trapezoids. [Image] bisects [Image]. [Image].
Prove: [Image]
[Image]

Write a flow proof.

Given: W is the midpoint of [Image] and [Image]. [Image].
Prove: [Image]
[Image]

Write a flow proof.

Given: [Image] is isosceles. [Image].
Prove: [Image]
[Image]

Write a two-column proof.

Given: Circle F. F is the center of the circle.
Prove: [Image]
[Image]

Write a two-column proof.

Given: A regular hexagon. M is the midpoint of [Image] and [Image].
Prove: [Image]
[Image]

Write a flow proof.

Given: A regular hexagon. M is the midpoint of [Image] and [Image]. [Image].
Prove: [Image]
[Image]

Write a two-column proof.

Given: W is the midpoint of [Image] and [Image].
Prove: [Image]
[Image]

Write a flow proof.

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

Q: Position and label the triangle on the coordinate plane.

right [Image] with hypotenuse [Image] 5a units and base [Image] 3a units
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
- [Image] (1. Use the origin as a vertex or center of the figure. 2. Place at least one side of a polygon on an axis. 3. Keep the figure within the first quadrant if possible. 4. Use coordinates that make computations as simple as possible.)
A: [Image]

Write a coordinate proof for the statement.

The segments joining the vertices to the midpoints of the legs of an isosceles triangle are congruent.

Write a flow proof.

Given: Two interlocking regular pentagons. [Image]. [Image] bisects [Image].
Prove: [Image]
[Image]

Write a two-column proof.

Given: R is the midpoint of [Image]. [Image].
Prove: [Image]
[Image]

The measures of the angles of [Image] are [Image].
a.      Draw a figure to illustrate [Image].
b.      Find the measure of each angle of [Image]. Explain.
c.      Prove that [Image] is an equilateral triangle.

Jan is creating a quilt made up of star-shaped composite quilting squares. The square is made up of four different triangles. Part of the square is shown below.
[Image]
a.      Find the measure of [Image], [Image], and [Image]. Explain.
b.      BD bisects AC. If [Image] in. and [Image] in., then what is the measure of the perimeter of the octagon? Explain.
c.      [Image] is isosceles. If [Image], what is [Image]? Explain.

Write a coordinate proof for the statement.

If a segment bisects the base of a right isosceles triangle, then the resulting two triangles are congruent.