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Geometry Lesson 4-1: Apply Triangle Sum Properties
Triangle: a polygon with three sides
Interior angles: original angles (inside)
Exterior angles: Angles that are linear pairs to interior angles
Corollary to a theorem: The acute angles of a right triangle are complementary
CLASSIFYING TRIANGLES BY SIDES
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
NO congruent
sides
At least 2
congruent sides
3 congruent sides
CLASSIFYING TRIANGLES BY ANGLES
Acute Triangle
Right
Triangle
Obtuse
Triangle
Equiangular
Triangle
*Notice that an
equilateral triangle is
also isosceles.
*An equiangular
triangle is also acute.
3 acute angles
1 right angel
1 obtuse angles
3 congruent
angles
Example 1: Classify ∆RST by its sides. Then determine if the triangle is a right triangle.
3-(-1)  4
-3-3
-6
-2
3
2-(-1) = 3
5-3
2
3 = -1
2
(Yes)
THEOREM 4.1: TRIANGLE SUM THEOREM
mA + mB + mC = 180
The sum of the measures of the interior angles of a triangle is 180.
THEOREM 4.2: EXTERIOR ANGLE THEOREM
m1 = m A + m B
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent
interior angles.
Example 2: Use the diagram at the right to find the measure of DCB and 1.
3x-9 = x + 73
2x = 82
X = 41
3x + 16 = 2x + 52
-16
-16
X = 36
COROLLARY TO THE TRIANGLE SUM THEOREM
mA + mB = 90
The acute angles of a right triangle are Complementary .
Example 3: The front face of the wheelchair ramp shown forms a right triangle. The measure of one
acute angle in the triangle is eight times the measure of the other. Find the measure of each acute angle.
8x + x = 90
X = 10
8 (10) = 80