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Triangle Similarity and Proportional Relationships Quiz

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In triangle ABC, angle A measures 40°, angle B measures 60°. What is the measure of angle C in degrees?

50°

Explanation

The sum of interior angles of a triangle is 180°.

If two triangles are similar, what can you say about their corresponding angles?

They have the same ratio

Explanation

Corresponding angles in similar triangles are equal.

In triangle PQR, angle P measures 50°, and angle Q measures 70°. What is the measure of angle R in degrees?

80°

Explanation

The sum of interior angles of a triangle is 180°.

In triangle ABC, if angle A measures 45° and angle B measures 60°, what is the measure of angle C in degrees?

75°

Explanation

The sum of interior angles of a triangle is 180°.

Which similarity criterion is used to prove that two triangles are similar if two angles of one triangle are equal to two angles of another triangle?

Angle-Angle (AA) Criterion

Explanation

Two angles of one triangle are equal to two angles of another triangle.

In triangle ABC and triangle DEF, angle A is congruent to angle D, and angle B is congruent to angle E. Which similarity criterion can be used to prove that the two triangles are similar?

Angle-Side-Angle (ASA) Criterion

Explanation

Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

If triangle ABC is similar to triangle DEF, and the ratio of the lengths of corresponding sides is 2:3, what is the ratio of their perimeters?

3:2

Explanation

The ratio of perimeters is the same as the ratio of corresponding sides.

In triangle DEF, if angle D measures 60° and angle F measures 80°, what is the measure of angle E in degrees?

40°

Explanation

The sum of interior angles of a triangle is 180°.

In triangle XYZ, angle X measures 50°, angle Y measures 70°. What is the measure of angle Z in degrees if the triangle is similar to triangle ABC where angle A measures 60° and angle B measures 80°?

40°

Explanation

Corresponding angles in similar triangles are equal.

#10

If triangle PQR is similar to triangle STU with a scale factor of 1:2, and the area of triangle PQR is 36 square units, what is the area of triangle STU?

144 square units

Explanation

The ratio of areas of similar triangles is the square of the scale factor.

#11

In triangle XYZ, if the ratio of the lengths of corresponding sides is 3:4 and the perimeter is 42 units, what is the perimeter of triangle XYZ?

48 units

Explanation

The perimeter of a triangle is the sum of its side lengths.

#12

If two triangles are similar, and one triangle has sides of length 6 cm, 8 cm, and 10 cm, what are the corresponding sides of the other triangle if the scale factor is 1:2?

12 cm, 16 cm, 20 cm

Explanation

Corresponding sides in similar triangles are proportional to the scale factor.

Triangle Similarity and Proportional Relationships Quiz

In triangle ABC, angle A measures 40°, angle B measures 60°. What is the measure of angle C in degrees?

If two triangles are similar, what can you say about their corresponding angles?

In triangle PQR, angle P measures 50°, and angle Q measures 70°. What is the measure of angle R in degrees?

In triangle ABC, if angle A measures 45° and angle B measures 60°, what is the measure of angle C in degrees?

Which similarity criterion is used to prove that two triangles are similar if two angles of one triangle are equal to two angles of another triangle?

In triangle ABC and triangle DEF, angle A is congruent to angle D, and angle B is congruent to angle E. Which similarity criterion can be used to prove that the two triangles are similar?

If triangle ABC is similar to triangle DEF, and the ratio of the lengths of corresponding sides is 2:3, what is the ratio of their perimeters?

In triangle DEF, if angle D measures 60° and angle F measures 80°, what is the measure of angle E in degrees?

In triangle XYZ, angle X measures 50°, angle Y measures 70°. What is the measure of angle Z in degrees if the triangle is similar to triangle ABC where angle A measures 60° and angle B measures 80°?

If triangle PQR is similar to triangle STU with a scale factor of 1:2, and the area of triangle PQR is 36 square units, what is the area of triangle STU?

In triangle XYZ, if the ratio of the lengths of corresponding sides is 3:4 and the perimeter is 42 units, what is the perimeter of triangle XYZ?

If two triangles are similar, and one triangle has sides of length 6 cm, 8 cm, and 10 cm, what are the corresponding sides of the other triangle if the scale factor is 1:2?

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