The document covers key concepts related to isosceles and equilateral triangles, including identification by side length and angle measures, as well as theorems associated with these triangle types. It outlines the isosceles triangle theorem and its converse, along with the equilateral triangle corollary and its converse. Practice problems are also provided for application of these concepts.

1. Isosceles and Equilateral Triangles
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:
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 TriangleIsosceles TriangleIsosceles TriangleIsosceles Triangle TheoremTheoremTheoremTheorem – if two sides of a triangle are
congruent, then the angles opposite the sides are
congruent.
ConverseConverseConverseConverse of the Isosceles Triangleof the Isosceles Triangleof the Isosceles Triangleof the Isosceles Triangle TheoremTheoremTheoremTheorem – 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 TriangleEquilateral TriangleEquilateral TriangleEquilateral Triangle CorollaryCorollaryCorollaryCorollary – if a triangle is equilateral, then
it is equiangular.
Converse of the Equilateral TriangleConverse of the Equilateral TriangleConverse of the Equilateral TriangleConverse of the Equilateral Triangle CorollaryCorollaryCorollaryCorollary – 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°