8-9 Congruent Figures
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpFind 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°
Course 2
8-9 Congruent Figures
52°
Problem of the Day
Draw triangles ABC and DEF so thata. AB = DE and BC = EFb. angle A is congruent to angle D.c. the triangles are not congruent.
Course 2
8-9 Congruent Figures
D E
F
A B
C
Learn to identify congruent figures and to use congruence to solve problems.
Course 2
8-9 Congruent Figures
Vocabulary
Side-Side-Side Rule
Insert Lesson Title Here
Course 2
8-9 Congruent Figures
Course 2
8-9 Congruent Figures
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.
Identify any congruent figures.
Additional Example 1A: Identifying Congruent Figures in the Real World
Course 2
8-9 Congruent Figures
The sides of the octagons are not congruent. Each side of the outer figure is larger than each side of the inner figure.
Identify any congruent figures.
Additional Example 1B: Identifying Congruent Figures in the Real World
Course 2
8-9 Congruent Figures
The sectors in the figure are congruent.
Identify any congruent figures.
Check It Out: Example 1A
Course 2
8-9 Congruent Figures
The sides of the figures are are not congruent.
Identify any congruent figures.
Check It Out: Example 1B
Course 2
8-9 Congruent Figures
The figures are not congruent. The figure on the outside is larger than the one on the inside.
Course 2
8-9 Congruent Figures
If all of the corresponding sides and angles of two polygons are congruent, then the polygons are congruent. For triangles in particular, the corresponding angles will always be congruent if the corresponding sides are 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.
Determine whether the triangles are congruent.
Additional Example 2: Identifying Congruent Triangles
Course 2
8-9 Congruent Figures
4 cm6 cm 5 cm
4 cm
4 cm
4 cmA
B
C
R
P
QAB = 4 cmBC = 4 cmAC = 6 cm
PQ = 4 cmPR = 4 cmRQ = 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.
Determine whether the triangles are congruent.
Check It Out: Example 2
Course 2
8-9 Congruent Figures
AC = 8 mAB = 6 mBC = 10 m
DF = 8 mDE = 6 mEF = 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 m10 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.
Course 2
8-9 Congruent Figures
For polygons with more than three sides, it is notenough 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, youcan find the missing measures in the figures.
Determine the missing measure in the set of congruent polygons.
Additional Example 3: Using Congruence to Find Missing Measures
Course 2
8-9 Congruent Figures
The missing angle measure is 110°.
The corresponding parts of congruent polygons are congruent.
The missing side length is 28mm.
Check It Out: Example 3A
Determine the missing measure in the set of congruent polygons.
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Course 2
8-9 Congruent Figures
6 ft
8 ft
5 ft120°135°
60°45°
6 ft
8 ft
5 ft
4 ft
120°135°45°
60°
The missing sidelength is 4 ft.
The correspondingsides are congruent.
?
Check It Out: Example 3B
Determine the missing measure in the set of congruent polygons.
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Course 2
8-9 Congruent Figures
The missing anglemeasure is 130°.
The correspondingangles 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°?
Lesson Quiz1. Identify any congruent figures.
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Course 2
8-9 Congruent Figures
2. Determine the missing measures in the set of congruent polygons.
none
a =11, b =6, c = 110°