1. Angle Side Theorems
Lesson 3.7

2. Theorem 20: If two sides of a triangle are congruent, the angles opposite the sides are congruent.
Then

3. Theorem 21: If two angles of a triangle are congruent, the sides opposite the angles are congruent.
Then

4. These are ways to prove an isosceles triangle:
Two sides are congruent.
Two angles are congruent.
Markings on a triangle:
Smaller side matches opposite <
Medium side opposite med <
Larger side opposite larger <

5. Theorem: If two sides are not congruent, then the angles opposite are not congruent.
Theorem: If two angles of a triangle are not congruent, their opposite sides are not congruent.

6. Equilateral and Equiangular are interchangeable in triangles
Equilateral and Equiangular are interchangeable in triangles. Not in all shapes!
Rhombus: equilateral but not equiangular.

7. Rectangle: equiangular but not equilateral.

8. What are the restrictions on the values of x?B C
Given: AC>AB
m B + m C <180
m B = 6x – 45
m C = 15 + x
What are the restrictions on the values of x?

9. You must solve two unknowns.
m B > m C
6x – 45 > 15 + x
5x > 60
x > 12
m B + m  C < 180
6x – x < 180
7x < 210
x < 30
Therefore, x must be between 12 and 30.