Classifying Triangles 4-1 Classifying Triangles Holt Geometry Warm Up Lesson Presentation Lesson Quiz

Do Now Classify each angle as acute, obtuse, or right. 1. 2. right 1. 2. 3. 4. If the perimeter is 47, find x and the lengths of the three sides. right acute obtuse x = 5; 8; 16; 23

Objectives Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths.

Vocabulary acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

Recall that a triangle ( ) is a polygon with three sides Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.

C A B AB, BC, and AC are the sides of ABC. A, B, C are the triangle's vertices.

Acute Triangle Three acute angles Triangle Classification By Angle Measures Acute Triangle Three acute angles

Three congruent acute angles Triangle Classification By Angle Measures Equiangular Triangle Three congruent acute angles

Right Triangle One right angle Triangle Classification By Angle Measures Right Triangle One right angle

Obtuse Triangle One obtuse angle Triangle Classification By Angle Measures Obtuse Triangle One obtuse angle

Example 1: Classifying Triangles by Angle Measures Classify BDC by its angle measures. obtuse Classify ABD by its angle measures. acute

Example 2 Classify FHG by its angle measures. equiangular

Equilateral Triangle Three congruent sides Triangle Classification By Side Lengths Equilateral Triangle Three congruent sides

At least two congruent sides Triangle Classification By Side Lengths Isosceles Triangle At least two congruent sides

Scalene Triangle No congruent sides Triangle Classification By Side Lengths Scalene Triangle No congruent sides

Remember! When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.

Example 3: Classifying Triangles by Side Lengths Classify EHF by its side lengths. isosceles Classify EHG by its side lengths. scalene

Example 4 Classify ACD by its side lengths. isosceles

Example 5: Using Triangle Classification Find the side lengths of JKL. JK=KL=23.3 JL = 44.5

Example 6 Find the side lengths of equilateral FGH. All = 17

Example 7: Application A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam? 7

Activity #1 1 2 3 Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180˚. 1 2 3

Activity #2 (alternative) 1 1 2 3 2 3 2 3 1

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. The smallest angle is opposite the shortest side while the largest angle is opposite the longest side. Y X Z

List the angles from smallest to largest: C B A 2 6 5 B C A 5 13 12

Can a triangle have the given lengths? B A 2 7 3 C B A 9 20 11

Can a triangle have the given lengths? B A 3 8 4 C B A 3 11 10

Describe possible lengths for the third side: 9, 12

Describe possible lengths for the third side: 4, 15 3, 4

Classify by Angles 60˚ 60˚ 60˚ Equiangular Acute Obtuse Right Classify by Sides Equilateral Isosceles Scalene

Classify by angles: x Acute 67˚ 48˚

Classify by angles: z 70˚ x Right y

Classify by angles and sides Obtuse / Scalene 5 2 120˚ 4 Classify by angles and sides Right/ Isosceles Equiangular/ Equilateral

Classify by angles and sides 125˚ Right / Scalene X

A triangle with a 90˚ angle has sides that are 3 cm, 4 cm, and 5 cm long. Classify the triangle by its angles and sides. Right / Scalene

Classify by angles and sides: 70˚ 42˚ Acute / Scalene

Classify by angles and sides: x 125˚ 160˚ Obtuse / Scalene