Isosceles Triangles

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Isosceles Triangles

• Section 4.2

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Definitions

• Vertex Angle the two congruent sides form the
  vertex angle
• Legs congruent sides of an isosceles triangle
• Base angles the other two angles are base
  angles
• Base the third side

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Theorem 4-1Isosceles Triangle Theorem

• If two sides of a triangle are congruent, then
  the angles opposite those sides are congruent

C
A B
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Theorem 4-2

• The bisector of the vertex angle of an isosceles
  triangle is the perpendicular bisector of the
  base

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Theorem 4-3Converse of Isosceles Theorem

• If two angles of a triangle are congruent, then
  the sides opposite the angles are congruent

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Corollary 1the Isosceles Triangle Theorem
If a triangle is equilateral then it is
equiangular
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Corollary 2Converse of Isosceles Triangle Theorem

• If a triangle is equiangular then it is
  equilateral

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Example 1

• Find x and y
• Theorem 4-2 states MO is perpendicular to lN so
  90
• x 27

M
x
N
y
63
O
l
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Example 2

• Find x
• 3x-53x-52x2 56
• 8x - 8 56
• 8x 64
• x 8

• ?

2x2
3x-5
Perimeter is 56
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Homework

• Day 1 Page 191 1-10,19,22-25
• Day 2 Page 191 26-33, 37-39,41,45