Download Lesson 6-2 (1)

December 11, 2014
Questions
December 11, 2014
Isosceles Triangles
What does it mean for a triangle to be isosceles?
Parts of an Isosceles Triangle
vertex angle
base angles
base
Isosceles Triangle Symmetry Theorem
The line containing the bisector of the vertex angle of an isosceles
triangle is a symmetry line for the triangle
Isosceles Triangle Coincidence Theorem
In an isosceles triangle, the bisector of the vertex angle, the
perpendicular bisector of the base, and the median to the base
determine the same line.
- bisector of vertex angle
- symmetry line
- perpendicular bisector of base
- median to the base
Isosceles Triangle Base Angles Theorem
If a triangle has two congruent sides, then the angles opposite them
are congruent.
Equilateral Triangle Symmetry Theorem
Every equilateral triangle has three symmetry lines, which are
bisectors of its angles (or equivalently, the perpendicular bisectors of
the sides).
Equilateral Triangle Angle Theorem
If a triangle is equilateral, then it is equiangular.
Corollary
Each angle of an equilateral triangle has measure 60º.
December 11, 2014
Examples
1. In ⊙Z below, m∠ZXY = 31º. What is the measure of m∠XZY?
X
Z
Y
A
2. Given: AB = AC in ∆ABC
Prove: m∠3 = m∠4
1
3
B
2
C
4
3. Is it possible for a triangle to have exactly two symmetry lines?
Explain.
December 11, 2014
Assignment: p. 313 (2-9, 12-18 even)