Transcript Lesson 4.5

Legs: congruent sides of an isosceles triangle
Base: third side of an isosceles triangle
Vertex: formed by the two congruent sides
Base Angles: two angles across from the legs; congruent in
isosceles triangles
Theorem 4-3 (Isosceles Triangle Thm): If two sides of
a triangle are congruent, then the angles opposite
those sides are congruent.
B  C
c
b
a
Given: 2 sides congruent
Prove: 2 angles congruent
Statements
1. XY ≅ 𝑋𝑍 and
𝑋𝐵 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑌𝑋𝑍
2. ∠1 ≅ ∠2
3. BX ≅ BX
4. ∆𝑌𝑋𝐵 ≅ ∆𝑍𝑋𝐵
5. ∠Y ≅ ∠𝑍
Reasons
1. Given
2. Def. of Angle Bisector
3. Reflexive Property
4. SAS
5. CPCTC
Theorem 4-4 (Converse of Isosceles Triangle
Thm): If two angles of a triangle are
congruent, then the sides opposite the angles
are congruent.
AB  AC
Given: 2 angles congruent
Prove: 2 sides congruent
Theorem 4-5: The bisector of the vertex angle
of an isosceles triangle is the perpendicular
bisector of the base.
Example: Find x and y.
Corollary: a statement that follows immediately from a theorem
Corollary to Thm 4-3: If a triangle is equilateral, then it is equiangular.
Corollary to Thm 4-4: If a triangle is equiangular, then it is equilateral.