warm up find the measure of the third angle in the triangle, given two angle measures
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7-5. Congruent Figures. 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°. 52°. 50°. Course 2. 7-5. Congruent Figures. Objective Today - PowerPoint PPT PresentationTRANSCRIPT
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
7-5 Congruent Figures
52°
Objective Today
You will learn to identify congruent figures and to use them to find missing measures.
Key Math TermCongruent polygons Congruent polygons – – Are polygons with Are polygons with the same shape and the same sizethe same shape and the same size
Course 2
7-5 Congruent Figures
Course 2
7-5 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.
Example 1: Identifying Congruent Triangles
Course 2
7-5 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.
Try This: Example 2
Course 2
7-5 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
7-5 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.
120 m
120 m
70 m 70 m
120 m
120 m
70 m70 m
145°145°35°
35°
If you know that two figures are congruent, youcan find the missing measures in the figures.
Determine the missing measures in the set of congruent polygons.
Additional Example 3A: Using Congruence to Find Missing Measures
Course 2
7-5 Congruent Figures
The missing side measure is 28 mm.
The correspondingsides are congruent.
Determine the missing measure in the set of congruent polygons.
Additional Example 3B: Using Congruence to Find Missing Measures
Course 2
7-5 Congruent Figures
The missing angle measure is 88°.
The corresponding angles are congruent.
Try This: Example 3A
Determine the missing measure in the set of congruent polygons.
Insert Lesson Title Here
Course 2
7-5 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 sidemeasure is 4 ft.
The correspondingsides are congruent.
Try This: Example 3B
Determine the missing measure in the set of congruent polygons.
Insert Lesson Title Here
Course 2
7-5 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 Quiz
1. Are the triangles congruent?
Insert Lesson Title Here
Course 2
7-5 Congruent Figures
A
B C
7 cm5 cm
8 cmF
D
E
5 cm
8 cm
8 cm
2. Determine the missing measures for the set of congruent polygons.
18
6
a
b
70°
110°
6 6
11110°
70° 70°
no
a =11, b =6, c = 110°
70°
110°
c
