4 4 isosceles triangle
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Some Theorems Based on Congruent Triangles
The Isosceles Triangle Theorems
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The Isosceles TriangleA triangle is isosceles iff it has at least two sides congruent.
vertex angle
legleg
base angles
base
Parts of an isosceles triangle:
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Theorem 4-1 The Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.– Can also be stated: The base angles of an
isosceles triangle are congruent.
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Corollaries to the Isosceles Triangle Theorem
Corollary 1– An equilateral triangle is also equiangular.
Corollary 2– An equilateral triangle has three 60° angles.
Corollary 3– The bisector of the vertex angle of an isosceles
triangle is perpendicular to the base at its midpoint.
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Theorem 4-2
If the base angles of a triangle are congruent, then the sides opposite those angles are congruent.
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Corollary to the Converse of the Isosceles Triangle Theorem
Corollary 1– An equiangular triangle is also equilateral.