Applying Triangle Sum Properties
Section 4.1
Triangles
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Triangles are polygons with three sides.
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There are several types of triangle:
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Scalene
Isosceles
Equilateral
Equiangular
Obtuse
Acute
Right
Scalene Triangles
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Scalene triangles do not have any congruent sides.
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In other words, no side has the same length.
6cm
3cm
8cm
Isosceles Triangle
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A triangle with 2 congruent sides.
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2 sides of the triangle will have the same length.
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2 of the angles will also have the same angle measure.
Equilateral Triangles
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All sides have the same length
Equiangular Triangles

All angles have the same angle measure.
Obtuse Angle
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Will have one obtuse angle.
Acute Triangle
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All angles are acute angles.
Right Triangle
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Will have one right angle.
Exterior Angles vs. Interior Angles

Exterior Angles are angles that are on the outside of a
figure.
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Interior Angles are angles on the inside of a figure.
Interior or Exterior?
Interior or Exterior?
Interior or Exterior?
Triangle Sum Theorem (Postulate Sheet)
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States that the sum of the interior angles is 180.
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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)
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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
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2x + 40 = x + 72
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2x = x + 32
x = 32
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Find x and y
46
o
8x - 1
3x + 13
2y
o
Page 221
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