1. Isosceles and Equilateral Triangles
Learning Target: I can use and apply the properties of Isosceles and Equilateral Triangles.

2. 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

3. C C A B A B If... AC≅BC Then... <A≅<B
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 B A C B A

4. Find the value of the variables.x0 x0 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
750 x0

5. C C A B A B Then... If... AC≅BC <A≅<B
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 B A C A B

6. Find the values of the variables.
100 x y0 x0
x=2x-6
x+6=2x
6=x
y=90
x+x+10+10=180
2x+20=180
2x=160
x=80
2x-6

7. C C A A D B D B If... AC≅BC and <ACD≅<BCD Then...
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 A B C D A B C D

8. What is the value of x? B x0 C D 540 A 54+x+x+54=180 108+2x=180 2x=72

9. 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.

10. If a triangle is equilateral, then the triangle is equiangular.
Corollary to Isosceles Triangle Theorem
Corollary to Converse of Isosceles Triangle Theorem
If a triangle is equilateral, then the triangle is equiangular.
If a triangle is equiangular, then the triangle is equilateral.

11. D B 500 F G C A E H Find the measure of these angles: m<BCA=60
m<DCE=65
m<DEF=115
m<BCD=55
m<BAG=120
m<GAH=60