Geometry CP, Oct 25

Classifying Triangles and Angles in Triangles

Book Section: 4-1 & 4-2

Essential Question: How are triangles classified and how are angles in

triangles related?

Standards: G-1.2, G-1.3, G-1.5, G-1.7, G-1.8

Triangles and Classification

• Triangle – A three sided polygon.

• Classifying Triangles

By Angle

By Sides

Classifying by Angles

Examples

Example 1A Classify Triangles by Angles

A. Classify the triangle as acute, equiangular, obtuse, or right.

Answer: The triangle has three congruent angles. It is an equiangular triangle.

Example 1B Classify Triangles by Angles

B. Classify the triangle as acute, equiangular, obtuse, or right.

Answer: One angle of the triangle measures 130°, so it is an obtuse angle. The triangle has an obtuse angle, so it is an obtuse triangle.

A. acute

B. equiangular

C. obtuse

D. right

Classify ΔACD as acute, equiangular, obtuse, or right.

Classifying by Sides

Example 3 Classify Triangles by Sides

ARCHITECTURE The triangle truss shown is modeled for steel construction. Classify ΔJMN, ΔJKO, and ΔOLN as equilateral, isosceles, or scalene.

Answer: ΔJMN has no congruent sides, so it is a scalene triangle. ΔJKO has no congruent sides, so it is a scalene triangle. ΔOLN has all sides congruent, so it is an equilateral triangle.

A. equilateral

B. isosceles

C. scalene

If point C is the midpoint of BD, classify ΔABC as equilateral, isosceles, or scalene.

Example 5 Finding Missing Values

ALGEBRA Find the measures of the sides of isosceles triangle KLM with base KL.

Triangle Angle Relationships

Example 1

Find the measure of 1, 2, And 3.

Exterior Angles of a Triangle

• An Exterior Angle of a triangle is an angle that

forms a linear pair with an interior angle (or angle

of) a triangle.

• Remote Interior Angles are angles that are not

adjacent to the exterior angle.

Examples

Exterior Angles of a Triangle

Corollaries

• Corollary – A theorem with a proof that follows as a

direct result of another theorem. These two follow

directly from the Triangle Angle-Sum Theorem.

Examples

Find the measure of each numbered

angle.

Examples

Classwork: Text p. 241, 21-26, 30-35;

p. 251, 17-20; 24-29

Homework: HW Due 10 29, part 1, 1-10

part 2, 3-11