Transcript Similarity and Congruence

Similarity and Congruence
Identifying Similarity and Congruence
Finding Missing Measures
POLYGONS
Irma Crespo 2010
Warm Up
Which are similar? Which are congruent?
SIMILAR
CONGRUENT
same shape; different size
same shape; same size
Congruence
Congruent polygons have the same
measures: same lengths and same angles.
93°
5.4 cm
38°
49°
49°
congruent triangles
Congruence
Matching parts are corresponding parts.
In congruent polygons, corresponding parts
are equal.
l
k
j
i
p
o
n
m
Similarity
Similar polygons have corresponding angles
with the same measure AND the ratio of
their corresponding sides are proportional.
A
6
14
B
14
J
1.5
M
C
6
D
3.5
K
1.5
3.5
L
Corresponding angles are
equal: each pair has 90°
Corresponding sides are
proportional.
4
AB
AC
CD
6 =
BD
14
=
JM
JK
KL
1.5
LM
3.5
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.
L
M
3
O
N
m
G
H
2
I
4
J
rectangle LMNO
rectangle GHIJ
LO = NO
GI
JI
3
2
= m
4
2m = 3(4)
2m = 12
m=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.
3
24
48
12
x
6
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/u
nits
• 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.