The Isosceles Triangle Theorems

1
The Isosceles Triangle Theorems

• Lesson 4.4
• Pre-AP Geometry

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Isosceles Triangle
A triangle with at least two congruent sides.
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The Isosceles Triangle Theorem

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

Base angles of an isosceles triangle are
congruent.
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The Isosceles Triangle Theorem

• COROLLARY An equilateral triangle is also
  equiangular.

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The Isosceles Triangle Theorem

• COROLLARY An equilateral triangle has three
  60 angles.

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The Isosceles Triangle Theorem

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

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CONVERSE ISOSCELES TRIANGLE THEOREM

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

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CONVERSE ISOSCELES TRIANGLE THEOREM

• COROLLARY An equiangular triangle is also
  equilateral.

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Written Exercises

• Problem Set 4.4A p.137 3, 4, 6, 9, 12, 14,
  15, 17, 22

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Written Exercises

• Problem Set 4.4B, p.138 16, 19, 21, 24, 27, 31