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Similarity

Description: This quiz covers the concept of similarity in geometry. It includes questions on identifying similar figures, finding scale factors, and solving problems involving similar triangles.
Number of Questions: 15
Created by:
Tags: geometry similarity scale factor similar triangles
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In a triangle ABC, the sides AB and AC are 6 cm and 8 cm respectively. If the triangle is similar to triangle DEF, where DE is 9 cm, what is the length of DF?

  1. 12 cm

  2. 15 cm

  3. 18 cm

  4. 21 cm

Show answer
Correct Option: C
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/DE = AC/DF. Substituting the given values, we get 6/9 = 8/DF. Solving for DF, we get DF = 18 cm.

Two triangles have corresponding sides of 3 cm, 4 cm, and 5 cm, and 6 cm, 8 cm, and 10 cm respectively. Are the triangles similar?

  1. Yes

  2. No

Show answer
Correct Option: A
Explanation:

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 3/6 = 1/2, 4/8 = 1/2, and 5/10 = 1/2. Since all the ratios are equal, the triangles are similar.

In a right triangle ABC, the hypotenuse AB is 10 cm and the side AC is 6 cm. If triangle PQR is similar to triangle ABC, where PQ is 15 cm, what is the length of QR?

  1. 9 cm

  2. 12 cm

  3. 15 cm

  4. 18 cm

Show answer
Correct Option: B
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 10/15 = 6/QR. Solving for QR, we get QR = 12 cm.

If two similar triangles have a scale factor of 3:5, what is the ratio of the area of the smaller triangle to the area of the larger triangle?

  1. 3:5

  2. 5:3

  3. 9:25

  4. 25:9

Show answer
Correct Option: C
Explanation:

The ratio of the areas of similar triangles is equal to the square of the scale factor. Therefore, the ratio of the area of the smaller triangle to the area of the larger triangle is (3/5)^2 = 9/25.

In a triangle ABC, the side AB is 12 cm and the side AC is 15 cm. If the triangle is similar to triangle DEF, where DE is 18 cm, what is the length of DF?

  1. 22.5 cm

  2. 27 cm

  3. 30 cm

  4. 36 cm

Show answer
Correct Option: B
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/DE = AC/DF. Substituting the given values, we get 12/18 = 15/DF. Solving for DF, we get DF = 27 cm.

Two triangles have corresponding sides of 5 cm, 12 cm, and 13 cm, and 10 cm, 24 cm, and 26 cm respectively. Are the triangles similar?

  1. Yes

  2. No

Show answer
Correct Option: A
Explanation:

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 5/10 = 1/2, 12/24 = 1/2, and 13/26 = 1/2. Since all the ratios are equal, the triangles are similar.

In a right triangle ABC, the hypotenuse AB is 20 cm and the side AC is 12 cm. If triangle PQR is similar to triangle ABC, where PQ is 30 cm, what is the length of QR?

  1. 18 cm

  2. 24 cm

  3. 30 cm

  4. 36 cm

Show answer
Correct Option: B
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 20/30 = 12/QR. Solving for QR, we get QR = 24 cm.

If two similar triangles have a scale factor of 2:3, what is the ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle?

  1. 2:3

  2. 3:2

  3. 4:9

  4. 9:4

Show answer
Correct Option: A
Explanation:

The ratio of the perimeters of similar triangles is equal to the scale factor. Therefore, the ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle is 2:3.

In a triangle ABC, the side AB is 8 cm and the side AC is 10 cm. If the triangle is similar to triangle DEF, where DE is 12 cm, what is the length of DF?

  1. 15 cm

  2. 18 cm

  3. 21 cm

  4. 24 cm

Show answer
Correct Option: B
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/DE = AC/DF. Substituting the given values, we get 8/12 = 10/DF. Solving for DF, we get DF = 18 cm.

Two triangles have corresponding sides of 7 cm, 24 cm, and 25 cm, and 14 cm, 48 cm, and 50 cm respectively. Are the triangles similar?

  1. Yes

  2. No

Show answer
Correct Option: A
Explanation:

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 7/14 = 1/2, 24/48 = 1/2, and 25/50 = 1/2. Since all the ratios are equal, the triangles are similar.

In a right triangle ABC, the hypotenuse AB is 30 cm and the side AC is 18 cm. If triangle PQR is similar to triangle ABC, where PQ is 45 cm, what is the length of QR?

  1. 27 cm

  2. 36 cm

  3. 45 cm

  4. 54 cm

Show answer
Correct Option: B
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 30/45 = 18/QR. Solving for QR, we get QR = 36 cm.

If two similar triangles have a scale factor of 4:5, what is the ratio of the area of the smaller triangle to the area of the larger triangle?

  1. 4:5

  2. 5:4

  3. 16:25

  4. 25:16

Show answer
Correct Option: C
Explanation:

The ratio of the areas of similar triangles is equal to the square of the scale factor. Therefore, the ratio of the area of the smaller triangle to the area of the larger triangle is (4/5)^2 = 16/25.

In a triangle ABC, the side AB is 10 cm and the side AC is 12 cm. If the triangle is similar to triangle DEF, where DE is 15 cm, what is the length of DF?

  1. 18 cm

  2. 20 cm

  3. 22 cm

  4. 24 cm

Show answer
Correct Option: B
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/DE = AC/DF. Substituting the given values, we get 10/15 = 12/DF. Solving for DF, we get DF = 20 cm.

Two triangles have corresponding sides of 9 cm, 15 cm, and 20 cm, and 18 cm, 30 cm, and 40 cm respectively. Are the triangles similar?

  1. Yes

  2. No

Show answer
Correct Option: A
Explanation:

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 9/18 = 1/2, 15/30 = 1/2, and 20/40 = 1/2. Since all the ratios are equal, the triangles are similar.

In a right triangle ABC, the hypotenuse AB is 40 cm and the side AC is 24 cm. If triangle PQR is similar to triangle ABC, where PQ is 60 cm, what is the length of QR?

  1. 36 cm

  2. 48 cm

  3. 60 cm

  4. 72 cm

Show answer
Correct Option: B
Explanation:

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 40/60 = 24/QR. Solving for QR, we get QR = 48 cm.

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