Midterm Review #4

The graph shows trapezoids ABCD, EFGH and PQRS. Select all statements that explain why the trapezoids are similar to each other.

• Trapezoid ABCD can be mapped onto PQRS by a clockwise rotation of 90 degrees with the center of origin, followed by a dilation with a scale factor of 1/2 and center at the origin, and finally a translation 4 units to the left and 4 units down.

• Trapezoid EFGH can be mapped onto PQRS by a dilation with a scale factor of 1/2 and center at the origin, followed by a reflection over the x-axis, then a translation 4 units to the left.

• Trapezoid PQRS can be mapped onto ABCD by a translation 4 units to the right and 4 units up, followed by a dilation with a scale factor of 2 with the center at the origin, and finally a 270° clockwise rotation about the origin.

• Trapezoid PQRS can be mapped onto EFGH by a dilation with a scale factor of 2 with the center at the origin, followed by a translation 8 units to the right and 8 units up.

• Trapezoid PQRS can be mapped onto ABCD by a clockwise rotation of 90°, followed by a dilation with the scale factor of 2 and center at the origin.

Answer explanation

Trapezoid ABCD can be mapped onto PQRS by a clockwise rotation of 90 degrees, followed by a dilation with a scale factor of 1/2 and a translation 4 units to the left and 4 units down.

Given ΔABC and ΔDEF as shown in the plane, select all statements that are true.

• ΔABC is a dilation of ΔDEF with a scale factor of 3/2.

• ΔABC is a dilation of ΔDEF with a scale factor of 2/3.

Answer explanation

ΔABC is a dilation of ΔDEF with a scale factor of 2/3. The perimeter ratio is 3/2. ∠F = ∠C.

Name the triangle congruence or similarity theorem/postulate that corresponds with the diagram.

• AAA (Angle-Angle-Angle) Congruence Theorem

• SAS (Side-Angle-Side) Similarity Theorem

• SSS (Side-Side-Side) Congruence Postulate

• AAS (Angle-Angle-Side) Congruence Theorem

Answer explanation

The diagram corresponds to the AAS (Angle-Angle-Side) Congruence Theorem, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Name the triangle congruence or similarity theorem/postulate that corresponds with the diagram.

• AAA (Angle-Angle-Angle) Congruence Theorem

• SAS (Side-Angle-Side) Similarity Theorem

• SSS (Side-Side-Side) Congruence Postulate

• AAS (Angle-Angle-Side) Congruence Theorem

Answer explanation

The diagram corresponds to the SSS (Side-Side-Side) Congruence Postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Name the triangle congruence or similarity theorem/postulate that corresponds with the diagram.

• AAA (Angle-Angle-Angle) Congruence Theorem

• SAS (Side-Angle-Side) Similarity Theorem

• SSS (Side-Side-Side) Congruence Postulate

• AAS (Angle-Angle-Side) Congruence Theorem

Answer explanation

The diagram corresponds to the SAS (Side-Angle-Side) Similarity Theorem, which states that if two triangles have two pairs of corresponding sides that are proportional and the included angles are congruent, then the triangles are similar.

ΔRST is reflected to form ΔR'S'T'. Select all of the statements that are true by CPCTC.

Answer explanation

By CPCTC, we can conclude that RT is congruent to R'T', RST is congruent to R'S'T', and angle R is congruent to angle R'.

Fill in the missing statements and reasons to complete the following proof.

a

b

d

e

f

c

g

SAS

CPCTC

1. Given

Reflexive Property

Fill in the missing statements and reasons to complete the following proof.

a

b

c

d

e

f

Vertical Angles Theorem

Given

Definition of Segment Bisector

SAS

Fill in the missing statements and reasons to complete the following proof.

a

b

c

d

e

f

g

h

CPCTC

Given

AAS

Solve for x in the diagram above.

Mathematical Equivalence

ON