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Handout 2
Math 121
01/23/2016
4.6 Isosceles, Equilateral, and Right Triangles
Theorem 4.6-1: Isosceles Base Angles Theorem If two sides of a triangle are congruent,
then the angles opposite those sides are congruent.
Theorem 4.6-2: Converse of Isosceles Base Angles Theorem If two angles of a triangle
are congruent, then the sides opposite those angles are congruent.
Theorem 4.6-3: Perpendicular Bisector of the Base of an Isosceles Triangle If a line
bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of
the base.
Corollary 4.6-4: If Equilateral then Equiangular Triangular (Corollary to theorem
4.6-1 If a triangle is equilateral, then the triangle is equiangular.
Corollary 4.6-5: If Equiangular then Equilateral Triangle (Corollary to Theorem
4.6-2) If a triangle is equiangular, then the triangle is equilateral.
Theorem 4.6-6: Hypotenuse-Leg (H-L) Theorem If the hypotenuse and a leg of one right
triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are
congruent.
5.1 Perpendicular And Angle Bisectors
Theorem 5.1-2: Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Theorem 5.1-3: Converse of the Perpendicular Bisector Theorem If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Theorem 5.1-5: Angle Bisector Theorem If a point is on the bisector of an angle, then the
point is equidistant from the sides of the angle.
Theorem 5.1-6: Converse of the Angle Bisector Theorem If a point in the interior of an
angle is equidistant from the sides of the angle, then the point is on the angle bisector.
5.2 - Bisectors of a Triangle
Theorem 5.2-1: Concurrency of Perpendicular Bisectors Theorem The perpendicular
bisectors of the sides of a triangle are of a triangle are concurrent at a point equidistant from the
vertices.
Theorem 5.2-2 Concurrency of the Angle Bisectors Theorem The bisectors of the angles
of a triangle are concurrent at a point equidistant from the sides of the triangle.
Winter 2017
Los Angeles City College
G. Dekermenjian
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