This document discusses identifying congruent figures and using congruence to find missing measures. It defines congruent figures as having the same shape and size. The Side-Side-Side Rule for triangles is explained - if the sides of two triangles are congruent, then the triangles are congruent. Examples are provided of identifying congruent triangles and polygons based on corresponding sides and angles. The document also provides examples of using known congruent figures to find missing side lengths or angle measures.

1. UNIT 4.1 CONGRUENTUNIT 4.1 CONGRUENT
FIGURESFIGURES

2. Warm Up
Find the measure of the third angle in
the triangle, given two angle measures.
1. 58°, 104°
2. 32°, 63°
3. 90°, 38°
4. 42°, 88°
18°
85°
50°
52°

3. Vocabulary
Side-Side-Side Rule

4. 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.
Look at the two patterns.

5. Identify any congruent figures.
A.
Additional Example 1: Identifying Congruent Figures in
the Real World
The sides of the octagons are not congruent.
Each side of the outer figure is larger than
each side of the inner figure.

6. Identify any congruent figures.
B.
Additional Example 1: Identifying Congruent Figures in
the Real World
The sectors in the figure
are congruent.

7. Two figures are congruent if they have
the same shape and size.
Remember!

8. Identify any congruent figures.
A.
Check It Out! Example 1
The sides of the figures are are not congruent.

9. Identify any congruent figures.
B.
Check It Out! Example 1
The figures are not congruent. The figure
on the outside is larger than the one on
the inside.

10. 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.

11. Determine whether the triangles are congruent.
Additional Example 2: Identifying Congruent
Triangles
4 cm
6 cm 5 cm
4 cm
4 cm
4 cm
A
B
C
R
P
Q
AB = 4 cm
BC = 4 cm
AC = 6 cm
PQ = 4 cm
PR = 4 cm
RQ = 5 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.

12. Determine whether the triangles are congruent.
Check It Out! Example 2
AC = 8 m
AB = 6 m
BC = 10 m
DF = 8 m
DE = 6 m
EF = 10 m
The notation ABC is read “triangle ABC.”
Reading Math
A
B
C F D
E
6 m 6 m
8 m8 m
10 m 10 m
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.

13. 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.

14. Determine the missing measure in the set of
congruent polygons.
A.
Additional Example 3: Using Congruence to Find
Missing Measures
The corresponding angles
of congruent polygons are
congruent.
The missing angle
measure is 110°.

15. The corresponding sides of
congruent polygons are
congruent.
The missing side length
is 28 mm.
Determine the missing measure in the set of
congruent polygons.
B.
Additional Example 3: Using Congruence to Find
Missing Measures

16. Check It Out! Example 3
Determine the missing measure in the set of
congruent polygons.
A.
6 ft
8 ft
5 ft120°135°
60°
45°
6 ft
8 ft
5 ft
4 ft
120°135°
45°
60°
The missing side
length is 4 ft.
The corresponding
sides are congruent.
?

17. Check It Out! Example 3
Determine the missing measure in the set of
congruent polygons.
B.
The missing angle
measure is 130°.
The corresponding
angles are congruent.
6 ft
6 ft
8 ft
4 ft
5 ft
5 ft
4 ft
8 ft
10 ft
10 ft
120°
130°110°
100° 80°
110°
80° 100°
120°
?

18. Lesson Quiz
1. Identify any congruent figures.
2. Determine the missing measures in the
set of congruent polygons.
none
a = 11, b = 6, c = 110°

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