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

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Presentation transcript:

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. Scalene Isosceles Equilateral Classified by Sides Acute Right Obtuse Equiangular Classified by Angles

Types of Triangles

Triangles in Architecture

Triangles in Architecture

Interior vs. Exterior Angles All the angles inside the triangle are called interior angles. 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.

Example 4 Find m<JKL.

Example 5 Find the values of a, b, and c.

Exercise 6: SAT What is the value of c?