Warm-Up

Warm-UpWarm-Up

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

4.1 Apply Triangle Sum 4.1 Apply Triangle Sum PropertiesProperties

Objectives:

1.To classify triangles by sides and angles

2.To find the measures of the interior and exterior angles of a triangle

PolygonsPolygons

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

3-D Rendering3-D Rendering

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

VocabularyVocabulary

Scalene Isosceles

Equilateral

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.

Acute Right

Obtuse Equiangular

Classified by Sides

Classified by Angles

Types of TrianglesTypes of Triangles

Triangles in ArchitectureTriangles in Architecture

Triangles in ArchitectureTriangles in Architecture

Interior vs. Exterior AnglesInterior vs. Exterior Angles

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

Triangle Sum TheoremTriangle Sum Theorem

The sum of the measures --?--.

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

Example 1Example 1

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

4060

2

1

C

A B

Example 2Example 2

Prove the Triangle Sum Theorem.

Given: ABC

Prove: ma + mb + mc = 180°

c

ba

A B

C

c

ba

A B

CF G

c

ba

A B

CF G

c

ba

A B

CF G

21 c

ba

A B

CF G

Example 3Example 3

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

y

x

Triangle Sum Theorem Triangle Sum Theorem CorollaryCorollaryThe acute angles of a right triangle are

complementary.

Investigation 2Investigation 2

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

Investigation 2Investigation 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:Exterior Angle Theorem:

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

Example 4Example 4

Find m<JKL.

Example 5Example 5

Find the values of a, b, and c.

40

75

a

b

c

120

Exercise 6: SATExercise 6: SAT

What is the value of c?

80

c

b

b

aa