Section 4.1 : Classifying Triangles EQ: How are the angle measures of triangle related?

Vocabulary B A C Definitions, Answers, Examples and Diagrams Triangle Vocabulary, Questions, Description of Examples Definitions, Answers, Examples and Diagrams   Triangle  Three-sided polygon Written ∆ABC Acute Triangle  Three acute angles (angles with degree less than 90) Equiangular Triangle 3 congruent acute angles B A C

Vocabulary Definitions, Answers, Examples and Diagrams Obtuse Triangle Vocabulary, Questions, Description of Examples Definitions, Answers, Examples and Diagrams   Obtuse Triangle  1 obtuse angle (angle > 90) Right Triangle 1 right angle (angle = 90)

Example 1: a) Classify the triangle as acute, equiangular, obtuse, or right. 3 acute angles that are all equal Equiangular b) Classify the triangle as acute, equiangular, obtuse, or right. 1 obtuse angle Obtuse Triangle

Example 2: Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.   Right Triangle ∠XYW + ∠WYZ = 90° 40° + 50° = 90°

You Try! 3 acute angles = acute triangle 1 right angle = right triangle 1 obtuse angle = obtuse triangle

Vocabulary Definitions, Answers, Examples and Diagrams Vocabulary, Questions, Description of Examples Definitions, Answers, Examples and Diagrams   Equilateral Triangle  3 congruent sides Isosceles Triangle At least 2 congruent sides Scalene Triangle No congruent sides

You Try! 3 congruent sides = equilateral triangle No congruent sides = scalene triangle 2 congruent sides = Isosceles triangle

Example 3: IF point Y is the midpoint of and WY = 3.0 units, classify ∆VWY as equilateral, isosceles, or scalene. Explain your reasoning. Scalene – no sides are equal

Example 4: a) Find the measures of the sides of isosceles triangle KLM with base 𝐾𝐿 Isosceles triangle means 2 sides are equal. So with base 𝐾𝐿 that means 𝐾𝑀 and 𝐿𝑀 are equal. Solve for d. 12−𝑑=4𝑑−13 𝑑=5 𝐾𝑀 =7 𝐿𝑀 =7 𝐾𝐿 =11

Example 4: B) Find the value of x and the measures of each side of an equilateral triangle ABC if AB = 6x – 8, BC = 7 + x, and AC = 13 – x. Equilateral triangle means all sides are equal. Set two equations equal to one another and solve. 6𝑥−8=7+𝑥 𝑥=3 𝐴𝐵 =10 𝐵𝐶 =10 𝐴𝐶 =10

You Try! 1. Classify each triangle. (Draw a picture to help!) B Isosceles triangle A C

You Try! 1. Classify each triangle. (Draw a picture to help!) D Right triangle E F

You Try! 1. Classify each triangle. (Draw a picture to help!) K Equilateral triangle J L

You Try! 1. Classify each triangle. (Draw a picture to help!) N No sides equal = scalene triangle M P

You Try! 1. Classify each triangle. (Draw a picture to help!) R S 1 obtuse angle = obtuse triangle Q