How to classify triangles and find the measures of their angles. Chapter 3.4GeometryStandard/Goal: 2.2, 4.1.

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Presentation transcript:

How to classify triangles and find the measures of their angles. Chapter 3.4GeometryStandard/Goal: 2.2, 4.1

1. Read, write, and discuss how to classify triangles and find the measure of their angles. 2. Read, write, and discuss how to use exterior angles of triangles. 3. Work on assignment.

Equiangular Triangle all angles are congruent Acute Triangle all angles are acute Obtuse Triangle one angle is obtuse and the other two angles are acute Right Triangle one right angle and the other two angles are acute

Equilateral Triangle all sides are congruent Isosceles Triangle at least two sides are congruent Scalene Triangle no sides are congruent

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

m ACB = 90Definition of right angle c + 70 = 90Angle Addition Postulate c = 20Subtract 70 from each side. Find c first, using the fact that ACB is a right angle. In triangle ABC, ACB is a right angle, and CD AB. Find the values of a, b, and c.

a + m ADC + c = 180Triangle Angle-Sum Theorem m ADC = 90Definition of perpendicular lines a = 180Substitute 90 for m ADC and 20 for c. a = 180Simplify. a = 70Subtract 110 from each side m CDB + b = 180 Triangle Angle-Sum Theorem m CDB = 90 Definition of perpendicular lines b = 180 Substitute 90 for m CDB b = 180 Simplify. b = 20 Subtract 160 from each side. To find b, use CDB. To find a, use ADC. (continued)

The three sides of the triangle have three different lengths, so the triangle is scalene. One angle has a measure greater than 90, so the triangle is obtuse. The triangle is an obtuse scalene triangle. Classify the triangle by its sides and its angles.

Exterior Angles of a Polygon is an angle formed by a side and an extension of an adjacent side. Example:

Remote interior angles the two nonadjacent interior angles Example:

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

Find m  1. m  = 125Exterior Angle Theorem m  1 = 35Subtract 90 from each side.

Explain what happens to the angle formed by the back of the chair and the armrest as you lower the back of the lounge chair. The exterior angle and the angle formed by the back of the chair and the armrest are adjacent angles, which together form a straight angle. As one measure increases, the other measure decreases. The angle formed by the back of the chair and the armrest increases as you lower the back of the lounge chair.

Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.