Download Theorems about Parallel Lines

Isosceles, Equilateral, and Right Triangles
Sec 4.6
GOAL:
To use properties of isosceles,
equilateral and right triangles
To use RHL Congruence Theorem
Definitions

Isosceles Triangle – a triangle that has at least two congruent
sides called legs.
Vertex Angle
Leg
Base
Angles

Leg
Base (noncongruent side)
If a triangle has three congruent sides, it is called an Equilateral
Triangle.
Each angle measures
60 degrees
Base Angles Theorem

Base Angles Theorem – If two sides of a triangle are congruent,
then the angles opposite them are congruent.
A
If AB  AC , then B  C
C
B
Converse of the Base Angles Theorem

Converse of the Base Angles Theorem – If two angles of a
triangle are congruent, then the sides opposite them are
congruent.
A
If B  C , then AB  AC
C
B
Corollaries

If a triangle is equilateral, then it is equiangular.

If a triangle is equiangular, then it is equilateral.
Is an equilateral triangle an isosceles triangle?
Is an isosceles triangle an equilateral triangle?
Example

Find x and y.
50
y
x
Hypotenuse – Leg (HL) Congruence

Hypotenuse – Leg (HL) Congruence – If the hypotenuse and a leg
of a right triangle are congruent to the hypotenuse and a leg of a
second right triangle , then the two triangles are congruent.
A
B
If AC  DF , and BC  EF then
ABC  DEF
or
If AC  DF , and AB  DE then
ABC  DEF
D
C
E
F
Two – Column Proof

Given: AB  DE , BC  EF
ABCand DEF are right angles
D
A
Prove:
ABC  DEF
B
C
E
F
Examples

Find x or y
x
y
50
30
3x
(2 x  4)
4y
(4 x  8)
Examples

Are you given enough information to prove the triangles
congruent?