# 3.3 Parallel Lines and the Triangle Angle-Sum Theorem - PowerPoint PPT Presentation

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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°

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

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