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

2. 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

3. 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)

4. 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

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

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

7. 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

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

9. 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

10. 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

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

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

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

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

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

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