Download 4.6 Isosceles and Equilateral Triangles

Warm Up
• Explain what information you would need
to prove two triangles congruent. Draw an
example to help guide your response.
I will be asking for people to share their
responses! (and I will be collecting this).
4.6 Isosceles and
Equilateral Triangles
Isosceles Triangle Properties
• The two congruent sides are called the legs of
an isosceles triangle, and the angle with the
sides that are the legs is called the vertex angle.
The side of the triangle opposite the vertex angle
is called the base. The two angles formed by the
base and the congruent sides are called the base
angles.
1 is the vertex angle.
2 and 3 are the
base angles.
Isosceles Triangle Theorems
Example 1
• a) Name two unmarked congruent angles.
• b) Name two unmarked congruent
segments.
Example 1 Continued
c) Which statement correctly names two
congruent angles?
a) PJM @ PMJ
b) JMK @ JKM
c) KJP @ JKP
d) PML @ PLK
Equilateral Triangle Corollaries
• The Isosceles Triangle Theorem leads to two
corollaries about the angles of an equilateral
triangle.
Example 2
a) Find mR
b) Find PR.
Example 3
• You can use the properties of equilateral
triangles and algebra to find missing values.
• Find the value of each variable.
Example 4
Prove using a two-column proof.
Given: HEXAGO is a regular polygon.
∆ONG is equilateral
N is the midpoint of GE
EX || OG
Prove: ∆ENX is equilateral.
Exit Slip
Write a two-column proof.
Given: DE || BC
1 @ 2
Prove: AB @ AC