4.6 Isosceles Triangles. Objectives. Use properties of isosceles triangles Use properties of equilateral triangles. Properties of Isosceles Triangles. The formed by the ≅ sides is called the vertex angle . The two ≅ sides are called legs . The third side is called the base .
If two s of a ∆ are ≅, then the sides opposite those s are ≅ (if B ≅ C, then AC ≅ AB).
By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So,Example 2:
a. Name two congruent angles.
b. Name two congruent segments.
EFG is equilateral, and bisects bisectsFindand
Each angle of an equilateral triangle measures 60°.
Since the angle was bisected,Example 3a:
is an exterior angle of EGJ.Example 3a:
Exterior Angle Theorem
EFG is equilateral, and bisects bisectsFindExample 3b:
Linear pairs are supplementary.
Subtract 75 from each side.
ABC is an equilateral triangle. bisectsYour Turn:
a. Find x.