Section 4.1 Apply Triangle Sum Properties
Goal  Classify triangles and find measures of their angles.
Classifying Triangles by Sides
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
_____ congruent sides
At least ____ congruent sides
_____ congruent sides
Classifying Triangles by Angles
Acute Triangle
Right Triangle
Obtuse Triangle
Equiangular Triangle
_____ acute angles
_____ right angle
_____ obtuse angles
_____ congruent angles
Example 1: Classify each triangle by its angles and sides:
a.
10
b.
c.
122º
10
6
29º
60º
10
29º
60º
8
60º
10
THEOREM 4.1: Triangle
Sum Theorem
THEOREM 4.2: Exterior
Angles Theorem
Corollary to the
Triangle Sum Theorem
mA + mB + mC =
__________
The sum of the measures of the
interior angles of a triangle is
______.
m1 = m_ __ + m__ _
The measure of an exterior angle of
a triangle is equal to the sum of the
measures of the two
NONADJACENT angles.
mA + mB = _____
The acute angles of a right
triangle are
_____________.
Section 4.1 Apply Triangle Sum Properties
Example 2: Use the Triangle Sum Theorem to find the missing angle measures.
a. mA
b. Find x
c. Find x and y
xº
85º
92º
100º
52º
20º
A
85º
yº
xº
Example 3: Use the Exterior Angle Theorem to find m2 in each problem below.
a.
b.
60º
60º
2
c.
155
º
125
º
2
2
64º
Example 4: In a right triangle, the measure of one of the acute angles is twice the measure of the
other. Sketch this and find the measures of the two acute angles in this right triangle.
Example 5: Use the diagram below to find the measure of DCB.
Checkpoint
1. Find mBAC and mBCA.
2. Find the measure of l in the diagram shown.