Similar Triangles and Proportions Practice

Find the missing length indicated. 

• 5

• 12

• 14

• 7

Find missing side

• 5

• 7

• 9

• 11

What is the measure of x?

• 12

• 15

• 6

• 9

The triangles are similar, solve for the question mark.

• 8

• 12.5

• 18

• 24

• 6 cm

• 12 cm

• 7.5 cm

• 10.5 cm

Answer explanation

Since the ratio of AB to DE is 3:4, and AB is 9 cm, DE would be 9 * (4/3) = 12 cm.

In triangle ABC and triangle XYZ, the ratio of the lengths of AB to XY is 2:3, and the ratio of the lengths of BC to YZ is 2:3. If angle B = angle Y, what is the ratio of the lengths of AC to XZ?

• 2:3

• 1:2

• Cannot be determined without knowing the angles

• 3:4

In triangles ABC and DEF, angle B is congruent to angle E and angle C is congruent to angle F. If BC = 10 cm and EF = 20 cm, what is the ratio of the area of triangle ABC to triangle DEF?

• 1:2

• 1:4

• 2:1

• 4:1

Answer explanation

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. Since EF:BC = 2:1, the ratio of the areas of triangle DEF to triangle ABC is 1:4.

Choose the similarity statement for the triangles.

• ΔMNL ∼ ΔOPQ

• ΔNOM ∼ ΔPQL

• ΔLMN ∼ ΔPQO

• ΔMLN ∼ ΔPQO

To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown.  What is AB to the nearest meter?

• 10

• 12

• 15

• 18

Find the value of x.

• 6.92

• 18.67

• 2.625

• 13.71