Applying Triangle Sum Properties
Section 4.1
Triangles
Triangles are polygons with three sides.
There are several types of triangle:
Scalene
Isosceles
Equilateral
Equiangular
Obtuse
Acute
Right
Scalene Triangles
Scalene triangles do not have any congruent sides.
In other words, no side has the same length.
6cm
3cm
8cm
Isosceles Triangle
A triangle with 2 congruent sides.
2 sides of the triangle will have the same length.
2 of the angles will also have the same angle measure.
Equilateral Triangles
All sides have the same length
Equiangular Triangles
All angles have the same angle measure.
Obtuse Angle
Will have one obtuse angle.
Acute Triangle
All angles are acute angles.
Right Triangle
Will have one right angle.
Exterior Angles vs. Interior Angles
Exterior Angles are angles that are on the outside of a
figure.
Interior Angles are angles on the inside of a figure.
Interior or Exterior?
Interior or Exterior?
Interior or Exterior?
Triangle Sum Theorem (Postulate Sheet)
States that the sum of the interior angles is 180.
We will do algebraic problems using this theorem.
The sum of the
angles is 180, so
x + 3x + 56= 180
4x + 56= 180
4x = 124
x = 31
Find the Value for X
2x + 15
2x + 15 + 3x + 90 = 180
5x + 105 = 180
3x
5x = 75
x = 15
Corollary to the Triangle Sum Theorem
(Postulate Sheet)
Acute angles of a right triangle are complementary.
3x + 10
20
3x + 10
5x +16
Exterior Angle Sum Theorem
The measure of the exterior angle of a triangle is equal to
the sum of the non-adjacent interior angles of the triangle
88 + 70 = y
158 = y
2x + 40 = x + 72
2x = x + 32
x = 32
Find x and y
46
o
8x - 1
3x + 13
2y
o
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