Download Isosceles and Equilateral Triangles Notes

Isosceles and Equilateral Triangles
Learning Target: I can use and apply the properties of Isosceles
and Equilateral Triangles.
vertex angle
Isosceles Triangles contain:
·vertex angle (top angle)
·legs (sides that make up vertex angle, these are always
congruent)
·base (side other than the legs)
·base angles (angles opposite vertex angles, these are
always congruent)
legs
base
base angles
Isosceles Triangle Theorem:
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
If...
AC≅BC
Then...
<A≅<B
C
A
C
B
A
B
Find the value of the variables.
x0
0
x
x0
1100
x+x+75=180
2x+75=180
2x=105
x=52.5
x+x+110=180
2x+110=180
2x=70
x=35
x0
750
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides oppoisite the angles are congruent.
Then...
AC≅BC
If...
<A≅<B
C
C
A
B
A
B
Find the values of the variables.
100
x
x0
2x-6
x=2x-6
x+6=2x
6=x
y0
y=90
x+x+10+10=180
2x+20=180
2x=160
x=80
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
If...
AC≅BC and <ACD≅<BCD
Then...
CD AB and AD≅BD
C
C
A
D
B
A
D
B
What is the value of x?
B
54+x+x+54=180
108+2x=180
2x=72
x=36
x0
C
540
A
D
A corollary is a theorem that can be proved easily using another theorem. Since a corollary is a
theorem, you can use it as a reason in a proof.
Corollary to Isosceles Triangle
Theorem
If a triangle is equilateral, then
the triangle is equiangular.
Corollary to Converse of Isosceles Triangle
Theorem
If a triangle is equiangular, then
the triangle is equilateral.
D
B
500
F
G
A
H
C
Find the measure of these angles:
m<BCA=60
m<DCE=65
m<DEF=115
m<BCD=55
m<BAG=120
m<GAH=60
E