Similarity and Congruence

Identifying Similarity and Congruence

Finding Missing Measures

POLYGONS

Irma Crespo 2010

Warm Up

Which are similar? Which are congruent?

SIMILAR

same shape; different size

CONGRUENT

same shape; same size

Congruence

Congruent polygons have the same measures: same lengths and same angles.

congruent triangles

93°

38°

49°

49°

5.4 cm

CongruenceMatching parts are corresponding parts.In congruent polygons, corresponding parts are equal.

l

kji

o

p

nm

ABJM

= ACJK

Similarity

Similar polygons have corresponding angles with the same measure AND the ratio of their corresponding sides are proportional.

A B6

DC 6

14 14

Corresponding angles are equal: each pair has 90°

L

J1.5M

3.5K

3.5

1.5 Corresponding sides are proportional.

CDKL

= BDLM

61.5

= 143.5

4

Similar Polygons? (OHP)

Are corresponding angles equal?

Are corresponding sides proportional?

Find Missing Measures

Given that rectangle LMNO is similar to rectangle GHIJ, find the missing measure.

J

G2I

H

4

3

L M

O Nm

LOGI

= NOJI

=32

rectangle LMNOrectangle GHIJ

m4

2m = 3(4)2m = 12m = 6

Finding Measures (OHP)

Summary

To determine if polygons are similar find out if the corresponding angles are similar and the corresponding sides are proportional.

To find missing measures on similar polygons, perform cross multiplication and solve for the variable.

Exit Slip

Find the missing measure for the similar polygons.

24

x

3

6

4812

Practice Worksheet

Complete the practice worksheet.

Work with a partner or on your own.

Submit completed worksheet for grading.

Solutions are discussed the next day.

Main Resources• http://www.absorblearning.com/mathematics/demo/

units• Math Connects: Concepts, Skills, and Problem

Solving; Teacher Edition; Course 3, Volume 1

Columbus:McGraw-Hill, 2009.• PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of

Education. Winter 2010.• Lesson plan and presentation were created under

the supervision of Mrs. Papanastasopoulos of O.W. Best Middle School in Dearborn Heights, Michigan.