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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.
