Understanding Similarity in Geometry

What is the definition of similar triangles?

• Triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

• Triangles are similar if they have one angle equal and the other two angles different.

• Triangles are similar if they are both acute triangles.

• Triangles are similar if they have the same area.

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

• The corresponding angles are supplementary.

• The corresponding angles are equal.

• The corresponding angles are unequal.

• The corresponding angles are complementary.

In triangle ABC, if angle A = angle D and angle B = angle E, what can you conclude about triangles ABC and DEF?

• Triangles ABC and DEF are similar.

• Triangles ABC and DEF have equal perimeters.

• Triangles ABC and DEF are congruent.

• Triangles ABC and DEF are identical.

If the sides of triangle XYZ are in the ratio 2:3, what can you say about triangle PQR if its sides are in the ratio 4:6?

• Triangle PQR is larger than triangle XYZ but not similar.

• Triangle PQR is similar to triangle XYZ.

• Triangle PQR has a different shape than triangle XYZ.

• Triangle PQR has sides in the ratio 1:2.5.

How do you determine if two polygons are similar?

• Two polygons are similar if their areas are equal.

• Two polygons are similar if they have the same number of sides.

• Two polygons are similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion.

• Two polygons are similar if one can be rotated to match the other.

If two similar triangles have a scale factor of 1:4, what is the ratio of their areas?

• 1:8

• 1:12

• 2:9

• 1:16

In similar triangles, if one triangle has a perimeter of 30 cm, what is the perimeter of the other triangle if the scale factor is 2:3?

• 45 cm

• 15 cm

• 30 cm

• 60 cm

If triangle ABC is similar to triangle DEF, and the length of side AB is 5 cm and side DE is 10 cm, what is the scale factor?

• 2

• 4

• 1

• 3

What is the relationship between the lengths of corresponding sides of similar figures?

• The lengths of corresponding sides are always different.

• The lengths of corresponding sides are equal.

• The lengths of corresponding sides are random.

• The lengths of corresponding sides are in proportion.

If two similar rectangles have lengths of 8 cm and 12 cm, what is the ratio of their widths if the ratio of their lengths is maintained?

• 1:2

• 2:3

• 4:5

• 3:4