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 .
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4.6 Isosceles Triangles
If two s of a ∆ are ≅, then the sides opposite those s are ≅ (if B ≅ C, then AC ≅ AB).
Name two congruent angles (not indicated).
Name two congruent segments (not indicated).
By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So,
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,
is an exterior angle of EGJ.
Exterior Angle Theorem
EFG is equilateral, and bisects bisectsFind
Linear pairs are supplementary.
Subtract 75 from each side.
ABC is an equilateral triangle. bisects
a. Find x.