Download Geo.11.21.14- 4.2.notebook

Geo.11.21.14­ 4.2.notebook
November 21, 2014
Warm Up
Classify each triangle.
4-2 Isosceles Triangles
p. 142
Objective: Use and apply properties of isosceles
triangles.
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Geo.11.21.14­ 4.2.notebook
November 21, 2014
Isosceles Triangle
vertex angle
-- 2 congruent sides
leg
leg
base angle
base angle
base
Theorem 4-1 Isosceles Triangle Thm
If 2 sides of a triangle are congruent, then the angles
opposite the sides are congruent.
C
If AC = BC, then
A
B
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Geo.11.21.14­ 4.2.notebook
November 21, 2014
Examples:
y
55°
40°
x
x
Theorem 4-3 Converse of the
Isosceles Triangle Thm
If 2 angles of a triangle are congruent, then the sides
opposite the angles are congruent.
If < A = < B, then
C
A
B
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Geo.11.21.14­ 4.2.notebook
November 21, 2014
Examples:
x-4
x
15
9
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Geo.11.21.14­ 4.2.notebook
November 21, 2014
Theorem 4-2
The bisector of the vertex angle of an isosceles triangle is
the perpendicular bisector of the base.
C
A
B
Examples:
63°
y
C
B
A
A
x°
C
x
y
20°
B
C
20°
A
x°
y
B
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Geo.11.21.14­ 4.2.notebook
November 21, 2014
Corollary to Isosceles Triangle Thm
If a triangle is equilateral, then it is equiangular.
Corollary to Converse of the Isosceles
Triangle Thm
If a triangle is equiangular, then it is equilateral.
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Geo.11.21.14­ 4.2.notebook
November 21, 2014
Examples:
32
x
x
y°
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HW # 39 p. 191-92 # 1-15, 22-25
** Draw diagram when needed!
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