Download 4.5 - Isosceles and Equilateral Triangles.notebook

4.5 ­ Isosceles and Equilateral Triangles.notebook
4.5: Isosceles & Equilateral Triangles
January 07, 2016
Date: 1/7
Isosceles Triangles
THEOREM 4­3: ISOSCELES TRIANGLES THEOREM:
If two sides of a triangle are congruent,
then the angles opposite those sides
are congruent.
THOEREM 4­4: CONVERSE OF THE ISOSCELES TRIANGLE THEOREM
If two angles of a triangle are congruent,
then sides opposite those angles
are congruent.
1
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
Ex 1) a). Is GH = HK? Explain.
b). Is HL = KJ? Explain.
2
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
THEOREM 4­5:
If a line bisects the vertex angle
of an isosceles triangle, then the line is also the
perpendicular bisector of the base.
3
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
Ex 2). What is the value of x?
a)
b)
4
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
EQUILATERAL & EQUIANGULAR TRIANGLES
COROLLARY TO THEOREM 4­3:
If a triangle is equilateral, then
the triangle is equiangular.
COROLLARY TO THEOREM 4­4:
If a triangle is equiangular, then
the triangle is equilateral.
5
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
Ex 3). What is the value of x and y?
6
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
Ex 4). Complete each statement:
a)
b)
c)
d)
7
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
Ex 5). Find each measure
a)
b)
c)
8
4.5 ­ Isosceles and Equilateral Triangles.notebook
January 07, 2016
Homework:
pg. 269 #1 – 12, 15 – 18, 21
9