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

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

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

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

5. 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.

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

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

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

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

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

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

12. Example 2
Classify FHG by its angle measures.
equiangular

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

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

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

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

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

18. Example 4
Classify ACD by its side lengths.
isosceles

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

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

21. 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

22. 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

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

24. 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

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

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

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

28. Describe possible lengths for the third side:
9, 12

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

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

31. Classify by angles: x
Acute
67˚
48˚

32. Classify by angles: z
70˚ x
Right y

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

34. Classify by angles and sides
125˚
Right / Scalene X

35. 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

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

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