4 4 isosceles triangle
Post on 20-Jan-2015
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Some Theorems Based on Congruent Triangles
The Isosceles Triangle Theorems
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:
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.
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.
Theorem 4-2
If the base angles of a triangle are congruent, then the sides opposite those angles are congruent.
Corollary to the Converse of the Isosceles Triangle Theorem
Corollary 1– An equiangular triangle is also equilateral.
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