Isosceles, Equilateral, and Right Triangles
Sec 4.6
GOAL:To use properties of isosceles, equilateral and right trianglesTo use RHL Congruence Theorem
Definitions Isosceles Triangle – a triangle that has at least two
congruent sides called legs.
If a triangle has three congruent sides, it is called an Equilateral Triangle.
LegLeg
Base (noncongruent side)
Base Angles
Vertex Angle
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
B
,If AB AC then B C
C
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
B
,If B C then AB AC
C
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.
xy
50
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.
,If AC DF and BC EF then ABC DEF
A
CB
D
FE
,
or
If AC DF and AB DE then ABC DEF
Two – Column Proof Given:
Prove:
,AB DE BC EF
ABCand DEF are right angles
ABC DEF A
CB
D
FE
Examples Find x or y
3050y
3xx
(4 8)x 4y
(2 4)x
Examples Are you given enough information to prove the triangles
congruent?
