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Applying Triangle Sum Properties

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Applying Triangle Sum Properties Section 4.1 Triangles Triangles are polygons with three sides. There are several types of triangle: Scalene Isosceles Equilateral ... – PowerPoint PPT presentation

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Title: Applying Triangle Sum Properties


1
Applying Triangle Sum Properties
  • Section 4.1

2
Triangles
  • Triangles are polygons with three sides.
  • There are several types of triangle
  • Scalene
  • Isosceles
  • Equilateral
  • Equiangular
  • Obtuse
  • Acute
  • Right

3
Scalene Triangles
  • Scalene triangles do not have any congruent
    sides.
  • In other words, no side has the same length.

6cm
3cm
8cm
4
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.

5
Equilateral Triangles
  • All sides have the same length

6
Equiangular Triangles
  • All angles have the same angle measure.

7
Acute Triangle
  • All angles are acute angles.

8
Right Triangle
  • Will have one right angle.

9
Obtuse Angle
  • Will have one obtuse angle.

10
Page 221
  • 1 - 10

11
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.

12
Interior or Exterior?
13
Interior or Exterior?
14
Interior or Exterior?
15
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 60
180
4x 60 180
4x 120
x 30
16
Find the Value for X
2x 15 3x 90 180
2x 15
5x 105 180
5x 75
3x
x 15
17
Corollary to the Triangle Sum Theorem (Postulate
Sheet)
  • Acute angles of a right triangle are
    complementary.

3x 10
3x 10 20 90
3x 30 90
20
3x 60
x 20
18
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

19
88 70 y
158 y
20
  • 2x 40 x 72
  • 2x x 32
  • x 32

21
Find x and y
38 7x 1 10x 9
10 x
39 7x 10x 9
10x 9
109
10(10) 9
39 3x 9
100 9
30 3x
109
10 x
109 y 180
y 71
22
Page 221
  • 14 26, 32
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