Triangles

Geometry

Mr. Zampetti

Unit 3, Day 1

Today’s Objectives

• To learn new strategies that will help find the measures of angles in a triangle

• To learn how to classify triangles

Triangle Activity

1. Draw and cut out a large triangle.

2. Number all three angles of the triangle

3. Tear of the angles

4. Place the 3 angles adjacent to each other to form one angle

• Compare your results with a partner.• Make a conjecture about the sum

of the angles of a triangle.

Theorem 2-1Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180.

Video: Sum of the Angles of a Triangle

Find the measure of the missing angle

http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gifhttp://maths.fallibroome.cheshire.sch.uk/triangle.jpg

http://www.gizapyramid.com/basic_triangle_w-angles.gif

x

x

Practice

• Find all Variables:

Practice

• Find all Variables:

Practice

• Find all variables

Definition

Exterior Angle: an angle formed by the side of a polygon and an extension of a side.

http://www.freemathhelp.com/images/lessons/exterior1.gif

Definition

Remote Interior Angle: the two nonadjacent interior angles to an exterior angle.

http://www.freemathhelp.com/images/lessons/exterior1.gif

Activity!

• Draw a triangle with an Exterior Angle like this:

• Measure all of the angles.• With a partner, make a conjecture about

the exterior angle and the remote interior angles.

Theorem 2-2Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Find the measure of the missing angle

http://www.kwiznet.com/px/homes/i/grade8/math/Grade_VIII_Triangles_And_Polygons_PB2_QuestionNo.5.gif

Find the measure of the missing angle

http://www.freemathhelp.com/images/lessons/exterior2.gif

Definition

Corollary: a statement that follows directly from a theorem.

Corollary to Theorem 2-2

The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.

Types of Triangles (by sides)

• Equilateral

• Isosceles

• Scalene

Equilateral Triangles

• Definition:– A triangle with three

congruent sides.

• Example:

Isosceles Triangles

• Definition:– A triangle with two

congruent sides.

• Example:

Scalene Triangles

• Definition:– A triangle with no

congruent sides.

• Example:

Types of Triangles (by angle)

• Equiangular

• Acute

• Right

• Obtuse

Equiangular Triangles

• Definition:– A triangle with three

congruent angles.

• Example:

Acute Triangles

• Definition:– A triangle whose

angles are all acute.

• Example:

Right Triangles

• Definition:– A triangle with one

right angle.

• Example:

Obtuse Triangles

• Definition:– A triangle with one

obtuse angle.

• Example:

Triangle Video

• Triangle video!!

Homework

Work Packet: Triangles