2.5.2 Isosceles and Equilateral Triangles

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

1. Isosceles and Equilateral Triangles
The student is able to (I can):
• Identify isosceles and equilateral triangles by si de length
and angle measure
• Use the Isosceles Triangle Theorem to solve proble ms
• Use the Equilateral Triangle Corollary to solve pr oblems

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

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

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

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

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