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Name _______________________________ Date ___________
Geometry
Congruent and Similar Figures
Write three conditions that two congruent polygons must share.
1. They have the same shape and size.
2. Their corresponding angles have the same measure.
3. Their corresponding sides have the same measure.
These two triangles are congruent. Draw slash marks to show which are the
corresponding sides and angles.
Write an equation stating that the two triangles are congruent. Be sure to name both
triangles by their corresponding vertices. Students may name the first triangle in any order, but
their equation should reflect the corresponding vertices. Correct answers include the following:
∆ CDE ≅ ∆ STR
∆ DCE ≅ ∆ TSR
∆ ECD ≅ ∆ RST
∆ EDC ≅ ∆ RTS
Tell how to find the measure of RS .
Use the measure of its corresponding part, side EC from ∆ ECD.
Write the name of each corresponding part.
EC
RS = ________
DE
TR = ________
∠C
∠ S = ________
∠E
∠ R = ________
Write the measure of each corresponding part.
9
RS = ________
© 2003 CompassLearning, Inc.
TR = ________
8.5
63°
∠ S = ________
Page 1
90°
∠ T = ________
Activity 8085/8127
Name _______________________________ Date ___________
Geometry
Congruent and Similar Figures
These two quadrilaterals are congruent. Fill in the blanks.
KLMJ
CDAB ≅ ___________
BADC
JMLK ≅ ___________
Use corresponding parts to find the missing measures.
6
AB = ________
2
DC = ________
7
JK = ________
4
ML = ________
45°
∠ D = ________
25°
∠ B = ________
155°
∠ K = ________
135°
∠ M = ________
Describe the ways in which two similar polygons are alike and different.
Two similar polygons have the same shape, but they may differ in size.
Their corresponding angles have the same measure.
Their corresponding sides are proportional.
© 2003 CompassLearning, Inc.
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Activity 8085/8127
Name _______________________________ Date ___________
Geometry
Congruent and Similar Figures
These two quadrilaterals are similar. Fill in the blanks.
OLMN
GFED ≈ ___________
FGDE
LONM ≈ ___________
Tell how to find the measure of ∠ O of the quadrilateral above.
Use the measure of its corresponding part, ∠ G, from quadrilateral GFED.
Write the name of each corresponding angle.
∠O
∠ G = ________
∠N
∠ D = ________
∠M
∠ E = ________
∠L
∠ F = ________
Write the measure of each corresponding angle.
92°
∠ D = ________
150°
∠ F = ________
64°
∠ O = ________
54°
∠ M = ________
The corresponding sides of similar figures are proportional. Write the names of the
corresponding sides of the two quadrilaterals above.
ON
GD ≈ ________
© 2003 CompassLearning, Inc.
NM
DE ≈ ________
ML
EF ≈ ________
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NM
FG ≈ ________
Activity 8085/8127
Name _______________________________ Date ___________
Geometry
Congruent and Similar Figures
How do you find missing lengths of sides of similar figures?
Write a proportion that compares the corresponding sides.
Write and solve a proportion to find the length of LO of the quadrilateral above. Show
your work. Round your answer to the nearest tenth.
15
16
=
5
n
16 x 5 = 15n
80 = 15n
80
= n
15
n = 5.3
LO = 5.3
Write and solve a proportion to find the length of ON of the quadrilateral above. Show
your work.
15
9
=
5
n
ON =
9 x 5 = 15n
45 = 15n
45
= n
15
n=3
3
© 2003 CompassLearning, Inc.
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Activity 8085/8127