Download Angle Side Theorems

Angle Side Theorems
Lesson 3.7
Theorem 20: If two sides of a triangle
are congruent, the angles opposite the
sides are congruent.
IF
Then
Theorem 21: If two angles of a triangle
are congruent, the sides opposite the
angles are congruent.
If
Then
These are ways to prove an
isosceles triangle:
1. Two sides are congruent.
2. Two angles are congruent.
Markings on a triangle:
Smaller side matches opposite <
Medium side opposite med <
Larger side opposite larger <
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.
Equilateral and Equiangular
are interchangeable in triangles.
Not in all shapes!
Rhombus: equilateral but not equiangular.
Rectangle: equiangular but not
equilateral.
A
B
6x-45
Given:
15+x
C
AC>AB
m B + m C <180
m B = 6x – 45
m C = 15 + x
What are the restrictions on the values of x?
You must solve two unknowns.
m B > m C
6x – 45 > 15 + x
5x > 60
x > 12
m B + m  C < 180
6x – 45 + 15 + x < 180
7x < 210
x < 30
Therefore, x must be
between 12 and 30.