Section 4.6 – Right, Isosceles and Equilateral Triangles
 An isosceles triangle has a pair of congruent sides.
 The congruent sides are called legs and the third side is
called the base.
 The angles opposite the legs are the base angles and the
third angle is the vertex angle.
Theorem 4-6: Base Angles Theorem
 If two sides of a triangle are congruent then the angles
opposite those sides are congruent.
Theorem 4.7: Converse of the Base Angles Theorem
 If two angles of a triangle are congruent, then the sides
opposite them are congruent.
Corollary to Theorem 4.6: If a triangle is equilateral
then it is equiangular.
Corollary to Theorem 4.7: If two angles of a triangle
are congruent, then the sides opposite them are
congruent.
Remember!
Hypotenuse
Leg
Leg
Theorem 4.8 – HL Congruence
 If the hypotenuse and a leg of one right triangle are
congruent to the corresponding parts of a second
right triangle, then the triangles are congruent.
A
B
D
C
E
IF BC = EF and AC = DF then ∆ABC  ∆DEF
F