Identify isosceles and equilateral triangles by side length and angle measure Use the Isosceles Triangle Theorem to solve problems Use the Equilateral Triangle Corollary to solve problems

1. Obj. 16 Isosceles and Equilateral
The student is able to (I can):
• Identify isosceles and equilateral triangles by side length
and angle measure
• Use the Isosceles Triangle Theorem to solve problems
• Use the Equilateral Triangle Corollary to solve problems

2. Parts of an Isosceles Triangle:
vertex angle
1
legs
2
3
base
base angles
Note: the base is the side opposite the
vertex angle, not necessarily the side on
the “bottom”.

3. Isosceles
Triangle
Theorem
If two sides of a triangle are congruent,
then the angles opposite the sides are
congruent.
B
AB ≅ CB ⇒ ∠A ≅ ∠C
A
Converse of
the Isosceles
Triangle
Theorem
C
If two angles of a triangle are congruent,
then the sides opposite those angles are
congruent.
E
F
∠D ≅ ∠F ⇒ DE ≅ FE
D

4. Equilateral
Triangle
Corollary
If a triangle is equilateral, then it is
equiangular.
B
AB ≅ BC ≅ CA
⇒ ∠A ≅ ∠B ≅ ∠C
A
C
Converse of
If a triangle is equiangular, then it is
the Equilateral equilateral.
Triangle
E
Corollary
∠D ≅ ∠E ≅ ∠F
⇒ DE ≅ EF ≅ FD
D
F

5. Practice
1. m∠S
K
2. m∠K
35°
S
Y
E
3. m∠S
S
22°
A

6. Practice
1. m∠S
= 35°
K
110°
2. m∠K
180 — (35 + 35)
180 — 70
110°
3. m∠S
180 — 22 = 158
158
= 79°
2
35°
35°
S
Y
E
S
79°
22°
A