Unit Six: Meaning of Similarity

Two similar figures have sides in the ratio of 2:3. If a side of the smaller triangle has a length of 7, what is the length of the corresponding side of the other triangle? 4 2/3 10 1/2 14 21

10 1/2

Select all that apply. Polygons must have which of the following characteristics to be considered similar? A 1:1 correspondence in vertices Corresponding angles are equal. Both polygons are the same shape Corresponding sides are proportional. Both polygons are the same size.

A 1:1 correspondence in vertices Corresponding angles are equal. Both polygons are the same shape Corresponding sides are proportional.

True/False - To be considered similar, two polygons must have corresponding sides that are equal.

False

Given: Triangle ABC is similar to Triangle RST Triangle DEF is similar to Triangle RST To Prove: Triangle ABC is similar to Triangle DEF STATEMENT: 1. ? 2. Angle A = Angle R, Angle D = Angle R Angle C = Angle T, Angle F = Angle T 3. Angle A = Angle D, Angle C = Angle F 4. ? REASON: 1. ? 2. ? 3. ? 4. ?

STATEMENT: 1. Triangle ABC is similar to Triangle RST Triangle DEF is similar to Triangle RST 4. Triangle ABC is similar to Triangle DEF REASON: 1. Given 2. Definition of similar triangles 3. Transitive Property 4. AA

If a line intersects two sides of a triangle, then it forms a triangle that is similar to the given triangle. always sometimes never

Sometimes

True/False - If the sides of one triangle are lengths 2, 4 and 6 and another triangle has sides of lengths 3, 6 and 9, then the triangles are similar.

True

True/False - If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

True

True/False - The three triangles in the following diagram are similar.

True

True/False - To be considered similar, two polygons must have corresponding angles that are equal.

True

True/False - To be considered similar, two polygons must have corresponding sides that are in proportion.

True

True/False - Triangles similar to the same triangle are similar to each other.

True