Embed Size (px)
Citation preview
Holt CA Course 1
9-9 Congruent Figures
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
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°
52°
Holt CA Course 1
9-9 Congruent Figures
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.
California Standards
Holt CA Course 1
9-9 Congruent Figures
Vocabulary
Side-Side-Side Rule
Holt CA Course 1
9-9 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.
Holt CA Course 1
9-9 Congruent Figures
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.
Holt CA Course 1
9-9 Congruent Figures
Identify any congruent figures.
B.
Additional Example 1: Identifying Congruent Figures in the Real World
The sectors in the figure are congruent.
Holt CA Course 1
9-9 Congruent Figures
Two figures are congruent if they have the same shape and size.
Remember!
Holt CA Course 1
9-9 Congruent Figures
Identify any congruent figures.
A.
Check It Out! Example 1
The sides of the figures are are not congruent.
Holt CA Course 1
9-9 Congruent Figures
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.
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.
Holt CA Course 1
9-9 Congruent Figures
Determine whether the triangles are congruent.
Additional Example 2: Identifying Congruent Triangles
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.
Holt CA Course 1
9-9 Congruent Figures
Determine whether the triangles are congruent.
Check It Out! Example 2
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 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.
Holt CA Course 1
9-9 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.
Holt CA Course 1
9-9 Congruent Figures
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°.
Holt CA Course 1
9-9 Congruent Figures
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
Holt CA Course 1
9-9 Congruent FiguresCheck 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 sidelength is 4 ft.
The correspondingsides are congruent.
?
Holt CA Course 1
9-9 Congruent FiguresCheck It Out! Example 3
Determine the missing measure in the set of congruent polygons.
B.
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°
?
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent FiguresLesson Quiz
1. Identify any congruent figures.
2. Determine the missing measures in the set of congruent polygons.
none
a = 11, b = 6, c = 110°
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
Holt CA Course 1
9-9 Congruent Figures
