Geometry Integrated with Algebra

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Geometry Integrated with Algebra

• Section 8-2
• The Triangle Sum Theorem

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Focus

• Apply the triangle sum theorem, quadrilateral
  theorems and exterior angle theorem

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Triangle Sum Theorem

• The sum of the measures of the angles of a
  triangle is _______.
• Why? Use the link to below to help you find the
  answer
• http//www.utc.edu/Faculty/Christopher-Mawata/geom
  /geom2.htm

180
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Triangle Sum Theorem

• The sum of the measures of the angles of a
  triangle is 180

m?1 m?2 m?3 180
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Example 1

• Find the measure of the missing angle in each
  triangle

C.
B.
A.
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Solution Example 1A

• Find the measure of the missing angle in each
  triangle

180 (90 50) 180 140 40
A.
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Solution Example 1B

• Find the measure of the missing angle in each
  triangle

180 (40 30) 180 70 110
B.
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Solution Example 1C

• Find the measure of the missing angle in each
  triangle

180 (70 50) 180 120 60
C.
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Example 2Using the Triangle Sum Theorem

• In the triangle , find

51
28
1
2
3
42
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Example 2Using the Triangle Sum Theorem

• In the triangle , find

180 - (51 42) 87
51
28
180 87 93
180 - (28 93) 59
1
59
2
93
3
87
42
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Quadrilateral Theorems

• The sum of the measures of the angles of a
  quadrilateral is ______.

Quadrilateral
Triangle
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Quadrilateral Theorems

• The sum of the measures of the angles of a
  quadrilateral is ______.

Quadrilateral
Triangle
180 180
360
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Quadrilateral Theorems

• If both pairs of opposite angles of a
  quadrilateral are equal in measure, then the
  quadrilateral is a _____________.

B
A
D
C
parallelogram
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Talk it Over 2

• A. Write an equation that represents the sum of
  the measures of the angles of ?ABC
• B. Solve the equation for x.
• C. Find the measures of the angles.

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Solution Talk it Over 2A

• A. Write an equation that represents the sum of
  the measures of the angles of ?ABC
• x 2x x 10 180

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Solution Talk it Over 2B

• B. Solve the equation for x.
• x 2x x 10 180
• 4x 10 180
• 4x 170
• x 42.5

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Solution Talk it Over 2c

• C. Find the measures of the angles.
• x 42.5

2(42.5) m?A 85
m?B 42.5
42.5 10 m?C 52.5
Check 42.5 85 52.5 180
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Measures of Angles of a Triangle

• The word triangle means three angles
• When the sides of a triangles are extended,
  however, other angles are formed
• The original 3 angles of the triangle are the
  interior angles
• The angles that are adjacent to interior angles
  are the exterior angles
• Each vertex has a pair of exterior angles

Original Triangle
ExteriorAngle
ExteriorAngle
Extend sides
InteriorAngle
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Investigating Angles of a Triangles
You can put the two torn angles together to
exactly cover one of the exterior angles
B
A
B
A
C
http//www.e-zgeometry.com/java/4.2extangle.asp
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Exterior Angle Theorem

• The measure of an exterior angle of a triangle is
  equal to the sum of the measures of the two
  remote (nonadjacent) interior angles

B
A
B
A
C
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Example 3

• Solve for x.
• What size is the exterior angle?

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Solution Example 3

• Solve for x.
• What size is the exterior angle?
• x 40 and 2x 5 are the remote interior angles
  of the exterior angle 8x
• x 40 2x 5 8x
• 3x 35 8x
• 35 5x
• x 7
• 8x 8(7) 56

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THE END