Similar Triangles Quiz

Are the triangles similar?

• Yes

• No

Answer explanation

The triangles are similar because they have the same shape but not necessarily the same size or orientation.

Tags

CCSS.HSG.SRT.A.2

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree.  How tall is the tree?

• 144 feet

• 72 feet

• 36 feet

• 48 feet

Answer explanation

To find the height of the tree, the distance from the mirror to the tree is the same as the distance from the mirror to the top of the tree. Therefore, the tree's height is half of the total distance, which is 72 feet.

Tags

CCSS.HSG.SRT.B.5

What is the measure of x?

• 12

• 15

• 6

• 9

Answer explanation

The measure of x is 9, as indicated in the correct answers section.

Tags

CCSS.HSG.CO.C.9

In triangle ABC and triangle DEF, angle A is congruent to angle D, and angle B is congruent to angle E. If the length of side AB is 5 cm and the length of side DE is 10 cm, what is the ratio of the similarity between the two triangles?

• 1:1

• 1:2

• 2:1

• 5:10

Answer explanation

The ratio of the similarity between the two triangles is 1:2 because the sides are in proportion to each other based on the given lengths of AB and DE.

Tags

CCSS.HSG.SRT.A.2

Triangle GHI is similar to triangle JKL. The sides of GHI are 7 cm, 14 cm, and 21 cm. If the shortest side of JKL is 21 cm, what is the length of the longest side of JKL?

• 42 cm

• 63 cm

• 84 cm

• 21 cm

Answer explanation

Since triangle GHI is similar to triangle JKL, the ratio of corresponding sides is the same. Therefore, if the shortest side of JKL is 21 cm, the longest side will be 21 cm * 3 = 63 cm.

Tags

CCSS.HSG.SRT.A.2

In the diagram, triangles MNO and PQR are similar. If MN = 8 cm, NO = 12 cm, and PQ = 4 cm, what is the length of PR?

• 6 cm

• 8 cm

• 12 cm

• 16 cm

Answer explanation

Since triangles MNO and PQR are similar, the ratio of corresponding sides is equal. Therefore, PR = (PQ/MN) * NO = (4/8) * 12 = 6 cm

Tags

CCSS.HSG.SRT.A.2

Triangles STU and VWX are similar. The ratio of the corresponding sides ST to VW is 3:4. If the perimeter of triangle STU is 45 cm, what is the perimeter of triangle VWX?

• 60 cm

• 30 cm

• 75 cm

• 90 cm

Answer explanation

Since the ratio of corresponding sides is 3:4, the perimeter of triangle VWX will be 4/3 times the perimeter of triangle STU. Therefore, the perimeter of triangle VWX is 60 cm (4/3 * 45 cm).

Given two similar triangles ABC and DEF, where the sides of ABC are 6 cm, 8 cm, and 10 cm, and the longest side of DEF is 15 cm. What is the length of the shortest side of DEF?

• 4.5 cm

• 6 cm

• 9 cm

• 12 cm

Answer explanation

The shortest side of the similar triangle DEF can be found by setting up a proportion with the corresponding sides of ABC. Using the ratio of sides, the shortest side of DEF is 9 cm.

Tags

CCSS.HSG.SRT.A.2

If triangles XYZ and PQR are similar and the angle X is 45 degrees, what is the measure of angle P?

• 45 degrees

• 90 degrees

• 135 degrees

• 180 degrees

Answer explanation

Since triangles XYZ and PQR are similar, angle X = angle P. Therefore, angle P is also 45 degrees.

Tags

CCSS.HSG.SRT.A.2

Triangles ABC and DEF are similar. The lengths of sides AB, BC, and CA are 5 cm, 12 cm, and 13 cm respectively. If side DE is 10 cm, what is the length of side EF?

• 24 cm

• 26 cm

• 12 cm

• 30 cm

Answer explanation

Since triangles ABC and DEF are similar, the ratio of corresponding sides is the same. Therefore, EF = (DE/AB) * BC = (10/5) * 12 = 24 cm.

Tags

CCSS.HSG.SRT.A.2