4.5 Isosceles and Equilateral Triangles

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4.5 Isosceles and Equilateral Triangles

• Chapter 4
• Congruent Triangles

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4.5 Isosceles and Equilateral Triangles

• Isosceles Triangle

Vertex Angle
Leg
Leg
Base Angles
Base
The Base Angles are Congruent
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Isosceles Triangles

• Theorem 4-3 Isosceles Triangle Theorem
• If two sides of a triangle are congruent, then
  the angles opposite those sides are congruent

B
ltA ltC
A
C
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Isosceles Triangles

• Theorem 4-4 Converse of the Isosceles
  Triangle Theorem
• If two angles of a triangle are congruent, then
  the sides opposite those angles are congruent

B
Given ltA ltC Conclude AB CB
A
C
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Isosceles Triangles

• Theorem 4-5
• The bisector of the vertex angle of an isosceles
  triangle is the perpendicular bisector of the
  base

B
Given ltABD ltCBD Conclude AD DC and BD is
- to AC
A
C
D
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Equilateral Triangles

• Corollary Statement that immediately follows a
  theorem

Corollary to Theorem 4-3 If a triangle is
equilateral, then the triangle is
equiangular Corollary to Theorem 4-4 If a
triangle is equiangular, then the triangle is
equilateral
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Using Isosceles Triangle Theorems

• Explain why ?RST is isosceles.

T
U
Given ltR ltWVS, VW SW Prove ?RST is
isosceles
R
W
V
S
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Using Algebra

• Find the values of x and y

M
)
)
y
N
x
O
63
L
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Landscaping

• A landscaper uses rectangles and equilateral
  triangles for the path around the hexagonal
  garden. Find the value of x.

x
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Practice

• Pg 213 1-16, 21-26