4'6 Isosceles, Equilateral, and Right Triangles

1
4.6 Isosceles, Equilateral, and Right Triangles

• Geometry
• Fall 2008

2
Objectives

• To use properties of isosceles, equilateral, and
  right triangles.

3
Isosceles Triangle
vertex angle
The two angles adjacent to the base are the base
angles. The angle opposite the base is the
vertex angle.
leg
leg
base angles
base
4
Theorem 4.6 Base Angle Theorem

• If two sides of a triangle are congruent, then
  the angles opposite them are congruent.

B
A
C
5
Theorem 4.7 Converse of the Base Angle Theorem

• If two angles of a triangle are congruent, then
  the sides opposite them are congruent.

B
A
C
6
Corollaries

• Corollary to Theorem 4.6
• If a triangle is equilateral, then it is
  equiangular.
• Corollary to Theorem 4.7
• If a triangle is equiangular, then it is
  equilateral.

A
B
C
7
Example 1 Using Equilateral and Isosceles
Triangles

• Find the value of x and y.

y
x
8
Example 2 Using Equilateral and Isosceles
Triangles

• Find the value of x and y.

50
x
y
9
Theorem 4.8 Hypotenuse-Leg (HL) Theorem

• If the hypotenuse and a leg of a right triangle
  are congruent to the hypotenuse and a leg of a
  second triangle, then the two triangles are
  congruent.

D
A
C
E
F
B
10
Assignment

• Page 239-240 1- 4, 8-10, 17-25 all