Geometry Chapter 4.6 Isosceles, Equilateral, and Right Triangles
I) Vocabulary:
A) Base angles - the two angles adjacent to the base of an isosceles triangle.
B) Vertex angles - the angle opposite the base of an isosceles triangle.
II) Theorems:
A) Base Angles Theorem: if two sides of a triangle are congruent, then the angles opposite them are congruent.
B) Converse of the Base Angles Theorem: if two angles of a triangle are congruent, the the sides opposite them are congruent.
C) Hypotenuse - Leg Congruence Theorem (HL = HL): if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.
Example: Given Δ ABC and ΔDEF are both right triangles, BC = EF and AC = DF,
then ΔABC = ΔDEF.
III) Corollaries:
A) If a triangle is equilateral, then it is equiangular.
B) If a triangle is equiangular, then it is equilateral.
