# Warm-Up - PowerPoint PPT Presentation

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Warm-Up. And speaking of the final frontier, what do you think is the shape of space?. 4.1 Apply Triangle Sum Properties. Objectives: To classify triangles by sides and angles To find the measures of the interior and exterior angles of a triangle. Polygons.

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Warm-Up

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### Warm-Up

And speaking of the final frontier, what do you think is the shape of space?

### 4.1 Apply Triangle Sum Properties

Objectives:

• To classify triangles by sides and angles

• To find the measures of the interior and exterior angles of a triangle

### Polygons

A closed plane figure is a polygon if it is formed by 3 or more line segments (sides), joined endpoint to endpoint (vertices) with each side intersecting exactly two others.

### 3-D Rendering

3-D rendering in digital graphics is based upon polygons.

### Vocabulary

As a group, define each of these types of triangles without your book. Draw a picture for each word and leave a bit of space for additions and revisions.

Classified by Sides

Classified by Angles

### Interior vs. Exterior Angles

All the angles inside the triangle are called interiorangles. If you extend the sides of the triangle, then the angles that form a linear pair with the interior angles are called exterior angles.

### Triangle Sum Theorem

The sum of the measures --?--.

Click the arrow buttons to watch the Flash animation of the Triangle Sum Theorem.

### Example 1

In ABC below, find the measures of  1 and 2.

### Example 2

Prove the Triangle Sum Theorem.

Given: ABC

Prove: ma + mb + mc = 180°

### Example 3

In the right triangle below, what is the value of x + y?

### Triangle Sum Theorem Corollary

The acute angles of a right triangle are complementary.

### Investigation 2

Use this Investigation to discover a relationship between an exterior angle of a triangle and its two remote interior angles.

### Investigation 2

How does the sum of the measures of the two remote interior angles compare with the measure of the exterior angle?

### Exterior Angle Theorem:

The measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles.

Find m<JKL.

### Example 5

Find the values of a, b, and c.

### Exercise 6: SAT

What is the value of c?