Ellis designed a rectangular envelope using

these measurements. What is w, the width

in centimeters in simplest radical form?

3√7

Figures that are similar (~) have the same

shape but not necessarily the same size.

Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

Oh look- a fancy box!

Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.

Writing Math

Identify the pairs of congruent angles

and corresponding sides. Name the

similar triangles.

N Q and P R.

By the Third Angles Theorem, M T.

0.5

A similarity ratio is the ratio of the lengths of

the corresponding sides of two similar polygons.

The similarity ratio of ∆ABC to ∆DEF is , or .

The similarity ratio of ∆DEF to ∆ABC is , or 2.

Determine whether the

RECTANGLES are similar. If so,

write the similarity ratio and a

similarity statement.

Determine whether the

polygons are similar. If

so, write the similarity

ratio and a similarity

statement.

What would be the

similarity shortcuts for

triangles?

Explain why the triangles

are similar and write a

similarity statement.

∆ABC ~ ∆DEF by AA ~

∆DEF and ∆HJK

Verify that the triangles are similar.

D H by the Definition of Congruent Angles.

Therefore ∆DEF ~ ∆HJK by SAS ~.

Verify that the triangles are similar.

∆PQR and ∆STU

Therefore ∆PQR ~ ∆STU by SSS ~.

Explain why ∆ABE ~ ∆ACD, and then find CD.

∆ABE ~ ∆ACD by AA ~.

Given: 3UT = 5RT and 3VT = 5ST

Prove: ∆UVT ~ ∆RST

You learned in Chapter 2 that the Reflexive,

Symmetric, and Transitive Properties of Equality

have corresponding properties of congruence. Do

these properties also hold true for similarity of

triangles?

Homework

• Worksheet