1. 5.4 – Equilateral and Isosceles Triangles

2. Using the Base Angles Theorem
A triangle is isosceles when it has at least two congruent sides.
The congruent sides are called the legs
The angle formed by the legs is called the vertex angle.
The third side is the base
The Two angles adjacent to the base are called the base angles.

3. Theorem 5.6 – Base angels theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent
If 𝐴𝐵 ≅𝐴𝐶, 𝑡ℎ𝑒𝑛<𝐵 ≅<𝐶.

4. Theorem 5.7 – Converse of the Base angles theorem
If two angels of a triangle are congruent, then the sides opposite them are congruent.
If <𝐵 ≅ <𝐶, 𝑡ℎ𝑒𝑛 𝐴𝐵 ≅𝐴𝐶.

5. Example 1 – Using the base angels theorem

6. You Try
HGK
HKG HK JK

7. Corollarires

8. Example 2 – Finding measures in a triangle

9. You try!
SOLUTION
Because the triangle is equiangular, it is also equilateral, meaning all of the side lengths are equal.
Therefore, the length of ST is also 5.

10. Example 3 – using isosceles and equilateral triangels

11. You try!
SOLUTION
X = 60
Y = 120