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3.3 Parallel Lines and the Triangle Angle-Sum Theorem. Chapter 3: Parallel and Perpendicular Lines. 3.3 Parallel Lines and the Triangle Angle-Sum Theorem. Theorem 3-7 Triangle Angle-Sum Theorem The angles in a triangle add up to 180 °. Triangle Angle-Sum Theorem. Find m <1. 1. 35 °.

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3.3 Parallel Lines and the Triangle Angle-Sum Theorem

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3.3 Parallel Lines and the Triangle Angle-Sum Theorem

Chapter 3: Parallel and Perpendicular Lines


3.3 Parallel Lines and the Triangle Angle-Sum Theorem

  • Theorem 3-7 Triangle Angle-Sum Theorem

    The angles in a triangle add up to 180°


Triangle Angle-Sum Theorem

Find m<1.

1

35°

65°


Triangle Angle-Sum Theorem

ΔMNP is a right triangle. <M is a right angle and m<N is 58°. Find m<P.


Using Algebra

G

Find the values of x, y, and z.

39°

21°

Solve for x:

65°

F

J

H

Solve for y:

Solve for z:


Classifying Triangles

Equiangular: All angles congruent

Equilateral: All sides congruent

60°

60°

60°

Acute Triangle: All angles are less than 90°

Right Triangle: One angle is 90°

Obtuse Triangle: One angle is greater than 90°


Classifying Angles

Isosceles: At least two sides congruent

Scalene: No sides congruent


Classifying a Triangle

Classify the triangle by its sides and angles.


Classifying a Triangle

Classify the triangle by its sides and angles.


Using Exterior Angles of Triangles

Exterior Angle of a Polygon

1 Exterior Angle

m<1 = m<2 + m<3

2

3

Remote Interior Angles

Theorem 3-8 Triangle Exterior Angle Theorem

The measure of the Exterior Angle is equal to the sum of the two

Remote Interior Angles


Using the Exterior Angle Theorem

Find each missing angle measure:

113°

40°

1

30°

70°

2

45°

45°

3


Homework

  • Pg 134 1-28


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