Apply Properties of Similar Triangles

In the accompanying diagram of equilateral triangle ABC, DE = 5 and DE || AB.  If AB is three times as long as DE, what is the perimeter of quadrilateral ABED?

• 20

• 30

• 35

• 40

Triangle ABC is similar to Triangle EFD. What scale factor is required to dilate triangle ABC so that its image, A'B'C' is congruent to triangle EFD?

• 2/5

• 1/2

• 2

• 3

Given a rectangle with right triangles inside, which triangle are similar to triangle AED? Select ALL that apply.

Triangle ABC can be taken to Triangle A'B'C' using rigid motions and a dilation. Select the true equation:

Is Line BC parallel to Line DE?

• Yes, because the sides are proportional

• No, because the sides are not proportional

Is Line BC parallel to Line DE?

• Yes, because the sides are proportional creating similar triangles

• No, because the sides are not proportional therefore the triangles are not similar

Given AC = 6, what sequence of transformations takes triangle AED to Triangle ABC?

• Dilate Triangle ADE using Center A and scale factor 1/2, then reflect over Line AD

• Dilate Triangle ADE using Center A and scale factor 2, then reflect over Line AC

• Rotate Triangle ADE clockwise around center A, then dilate by scale factor 3/2

• Reflect Triangle ADE over Line AD, then dilate using center E by scale factor 3/2

Triangle DEF is formed by connecting the midpoints of the sides of Triangle ABC. The lengths of DEF are shown. What are 2 things you know for sure about side BC?

• BD is perpendicular to DE

• BC is parallel to DF

• BA is 8 units

• BC is 8 units

Apply the properties of similar triangles to find the missing value: In Triangle LMN, the length of side LK is 8 cm, and the length of side MN is 12 cm. If Triangle LMN is similar to Triangle PQR, what is the length of side PQ?

• The length of side PQ is 10 cm.

• The length of side PQ is 18 cm.

• The length of side PQ is 15 cm.

• The length of side PQ is 20 cm.

Solve for the missing side length in the following similar triangles: Triangle ABC has side lengths of 6 cm, 8 cm, and 10 cm, and Triangle DEF has side lengths of 9 cm, 12 cm, and x cm. What is the value of x?

• 25

• 15

• 20

• 7