Download 9.9 Congruent Figures

9-9 Congruent Figures
California
Standards
Extension of
MG2.2 Use the
properties of complementary and
supplementary angles and the sum of the
angles of a triangle to solve problems
involving an unknown angle.
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9-9 Congruent Figures
Vocabulary
Side-Side-Side Rule
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9-9 Congruent Figures
Look at the two patterns. Which center circle do you
think is bigger? In spite of appearances, the two center
circles are congruent. Their apparent differences are
optical illusions. One way to determine whether figures
are congruent is to see if one figure will fit exactly over
the other one.
Holt CA Course 1
9-9 Congruent Figures
Teacher Example 1A: Identifying Congruent Figures in the
Real World
Identify any congruent figures.
A.
The sides of the octagons are not congruent.
Each side of the outer figure is larger than
each side of the inner figure.
Holt CA Course 1
9-9 Congruent Figures
Teacher Example 1B: Identifying Congruent Figures in the
Real World
Identify any congruent figures.
B.
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The sectors in the figure
are congruent.
9-9 Congruent Figures
Remember!
Two figures are congruent if they have
the same shape and size.
Holt CA Course 1
9-9 Congruent Figures
Student Practice 1A:
Identify any congruent figures.
A.
The sides of the figures are are not congruent.
Holt CA Course 1
9-9 Congruent Figures
Student Practice 1B:
Identify any congruent figures.
B.
The figures are not congruent. The figure
on the outside is larger than the one on
the inside.
Holt CA Course 1
9-9 Congruent Figures
If all of the corresponding sides and
angles of two polygons are congruent,
then the polygons are congruent. For
triangles, if the corresponding sides are
congruent, then the corresponding
angles will always be congruent. This is
called the Side-Side-Side Rule.
Because of this rule, when determining
whether triangles are congruent, you
only need to determine whether the
sides are congruent.
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9-9 Congruent Figures
Teacher Example 2: Identifying Congruent Triangles
Determine whether the triangles are congruent.
AB = 4 cm
BC = 4 cm
AC = 6 cm
PQ = 4 cm
PR = 4 cm
RQ = 5 cm
4 cm
B
4 cm
C
6 cm
A
Q
5 cm
R
4 cm
P
4 cm
The triangles are not congruent. Although two sides
in one triangle are congruent to two sides in the
other, the third sides are not congruent.
Holt CA Course 1
9-9 Congruent Figures
Student Practice 2:
Determine whether the triangles are congruent.
AC = 8 m
DF = 8 m
AB = 6 m
DE = 6 m
BC = 10 m EF = 10 m
B
6m
E
10 m 10 m
6m
A8 m C F 8 m D
By the Side-Side-Side Rule,
ABC is congruent to
DEF, or
ABC 
DEF. If you flip one triangle, it will fit exactly over
the other.
Reading Math
The notation ABC is read “triangle ABC.”
Holt CA Course 1
9-9 Congruent Figures
For polygons with more than three sides, it is not
enough to compare the measures of their sides.
For example, the corresponding sides of the
figures below are congruent, but the figures are
not congruent.
If you know that two figures are congruent, you
can find the missing measures in the figures.
Holt CA Course 1
9-9 Congruent Figures
Teacher Example 3: Using Congruence to Find
Missing Measures
Determine the missing measure in the set of
congruent polygons.
A.
The corresponding angles
of congruent polygons are
congruent.
The missing angle
measure is 110°.
Holt CA Course 1
9-9 Congruent Figures
Teacher Example 3: Using Congruence to Find
Missing Measures
Determine the missing measure in the set of
congruent polygons.
B.
The corresponding sides of
congruent polygons are
congruent.
The missing side length
is 28 mm.
Holt CA Course 1
9-9 Congruent Figures
Student Practice 3A:
Determine the missing measure in the set of
congruent polygons.
A.
?
120° 135°
The corresponding
sides are congruent.
The missing side
length is 4 ft.
6 ft
45°
60°
8 ft
8 ft
45°
5 ft
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5 ft
60°
6 ft
135°120°
4 ft
9-9 Congruent Figures
Student Practice 3B:
Determine the missing measure in the set of
congruent polygons.
B.
The corresponding
angles are congruent.
The missing angle
measure is 130°.
5 ft
6 ft
130° 110°
120°
4 ft 100°
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80°
10 ft
10 ft
100° 4 ft
80°
120°
8 ft
110° ? 5 ft
6 ft
8 ft
9-9 Congruent Figures
Lesson Quiz
1. Identify any congruent figures.
none
2. Determine the missing measures in the
set of congruent polygons.
a = 11, b = 6, c = 110°
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