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

2. Section 4-1: Classifying Triangles

3. What we’re going to learn…
How do classify triangles based on the measures of their angles and the length of their sides.
How to use triangle classifications to find measures of angles and lengths of sides.

4. Aligning SC Standards
G-1.8: Connect geometry with other branch of mathematics
G-3.1: Carry out a procedure to compute the perimeter of a triangle.
G-3.4: Apply properties of isosceles and equilateral triangles to solve problems.

5. What do you know? (Activate Prior Knowledge)
about triangles?
What do you THINK you know about triangles?
Students get in tribes and discuss collaboratively what they know about triangles and what they kind of know about triangles. Students will quickly brainstorm on their own first and then create a list for the group as a whole. (3 min.) As a whole group (class), we will discuss and fill in this chart on the smart board. Teacher will walk the room and get a student to fill in the chart.

6. What you WILL know? (Lesson Preview)*
acute triangle
equiangular triangle
right triangle
obtuse triangle
equilateral triangle
isosceles triangle
scalene triangle
Pass out graphic organizer for notes

7. 2 Ways to Classify Triangles
By Angles
By Sides

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

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

10. Classifying Triangles by Angles
Equiangular
All the angles are congruent

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

12. Classifying Triangles by Angles
Acute
All the angles are acute

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

14. Classifying Triangles by Angles
Right
One angle is right or 90°

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

16. Classifying Triangles by Angles
Obtuse
One angle is obtuse

17. Examples – Classifying Triangles by Angles
33°
57°
Classify the triangle to the left.
Right Triangle

18. Examples – Classifying Triangles by Angles
Classify the triangle to the left.
60 °
60°
60°
Equiangular

19. Examples – Classifying Triangles by Angles
Classify the triangle to the left.
Obtuse Triangle

20. Examples – Classifying Triangles by Angles
Classify the triangle to the left.
83.1°
44.7°
52.2°
Acute Triangle

21. You Try – Classifying Triangles by Angles
60 °
60°
Classify the triangle to the left.
Equiangular

22. You Try – Classifying Triangles by Angles
45°
Classify the triangle to the left.
Right Triangle

23. You Try – Classifying Triangles by Angles
Classify the triangle to the left.
88°
45°
47°
Acute Triangle

24. You Try – Classifying Triangles by Angles
Classify the triangle to the left.
110°
Obtuse Triangle

25. Example 1A: Classifying Triangles by Angle Measures
Classify BDC by its angle measures.
B is an obtuse angle.
B is an obtuse angle. So BDC is an obtuse triangle.

26. Example 1B: Classifying Triangles by Angle Measures
Classify ABD by its angle measures.
ABD and CBD form a linear pair, so they are supplementary.
Therefore mABD + mCBD = 180°. By substitution, mABD + 100° = 180°. So mABD = 80°. ABD is an acute triangle by definition.

27. Check It Out! Example 1
Classify FHG by its angle measures.
EHG is a right angle. Therefore mEHF +mFHG = 90°. By substitution, 30°+ mFHG = 90°. So mFHG = 60°.
FHG is an equiangular triangle by definition.

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

29. Classifying Triangles by Sides
Equilateral
All sides are congruent

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

31. Classifying Triangles by Sides
Isosceles
2 sides are congruent

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

33. Classifying Triangles by Sides
Scalene
NO sides are congruent

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

35. Examples - Classifying Triangles by Sides
Classify the triangle to the right.
ISOSCELES

36. Examples - Classifying Triangles by Sides
Classify the triangle to the right.
SCALENE

37. Examples - Classifying Triangles by Sides
Classify the triangle to the right.
EQUILATERAL

38. You Try - Classifying Triangles by Sides
Classify the triangle to the right.
SCALENE

39. You Try - Classifying Triangles by Sides
Classify the triangle to the right.
EQUILATERAL

40. You Try - Classifying Triangles by Sides
Classify the triangle to the right.
ISOSCELES

41. Example 2A: Classifying Triangles by Side Lengths
Classify EHF by its side lengths.
From the figure, So HF = 10, and EHF is isosceles.

42. Example 2B: Classifying Triangles by Side Lengths
Classify EHG by its side lengths.
By the Segment Addition Postulate, EG = EF + FG = = 14. Since no sides are congruent, EHG is scalene.

43. Classify ACD by its side lengths.
Check It Out! Example 2
Classify ACD by its side lengths.
From the figure, So AC = 15, and ACD is isosceles.

44. Examples- Classifying Triangles Both Ways
Classify the triangle to the right.
OBTUSE SCALENE
30°
33°
117°

45. Examples- Classifying Triangles Both Ways
Classify the triangle to the right.
48.5°
83°
Acute
IsoscELES

46. Examples- Classifying Triangles Both Ways
Classify the triangle to the right.
60°
Acute
Equilateral
60°
equiangular
Equilateral
60°

47. You Try - Classifying Triangles Both Ways
Classify the triangle to the right.
RIGHT SCALENE
57°
90°
33°

48. You Try - Classifying Triangles Both Ways
Classify the triangle to the right.
45°
RIGHT
ISOSCELES
45°

49. You Try- Classifying Triangles Both Ways
Classify the triangle to the right.
Acute
SCALENE
61°
41°
78°

50. Example 3: Using Triangle Classification
Find the side lengths of JKL.
Step 1 Find the value of x.
Given.
JK = KL
Def. of  segs.
Substitute (4x – 10.7) for JK and (2x + 6.3) for KL.
4x – 10.7 = 2x + 6.3
Add 10.7 and subtract 2x from both sides.
2x = 17.0
x = 8.5
Divide both sides by 2.

51. Example 3 Continued
Find the side lengths of JKL.
Step 2 Substitute 8.5 into the expressions to find the side lengths.
JK = 4x – 10.7
= 4(8.5) – 10.7 = 23.3
KL = 2x + 6.3
= 2(8.5) = 23.3
JL = 5x + 2
= 5(8.5) + 2 = 44.5

52. Check It Out! Example 3
Find the side lengths of equilateral FGH.
Step 1 Find the value of y.
Given.
FG = GH = FH
Def. of  segs.
Substitute
(3y – 4) for FG and (2y + 3) for GH.
3y – 4 = 2y + 3
Add 4 and subtract 2y from both sides.
y = 7

53. Check It Out! Example 3 Continued
Find the side lengths of equilateral FGH.
Step 2 Substitute 7 into the expressions to find the side lengths.
FG = 3y – 4
= 3(7) – 4 = 17
GH = 2y + 3
= 2(7) + 3 = 17
FH = 5y – 18
= 5(7) – 18 = 17

54. Example 4: 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?
The amount of steel needed to make one triangle is equal to the perimeter P of the equilateral triangle.
P = 3(18)
P = 54 ft

55. Example 4: Application Continued
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?
To find the number of triangles that can be made from 420 feet of steel beam, divide 420 by the amount of steel needed for one triangle.
420  54 = triangles
7 9
There is not enough steel to complete an eighth triangle. So the steel mill can make 7 triangles from a 420 ft. piece of steel beam.

56. Check It Out! Example 4a
Each measure is the side length of an equilateral triangle. Determine how many 7 in. triangles can be formed from a 100 in. piece of steel.
The amount of steel needed to make one triangle is equal to the perimeter P of the equilateral triangle.
P = 3(7)
P = 21 in.

57. Check It Out! Example 4a Continued
Each measure is the side length of an equilateral triangle. Determine how many 7 in. triangles can be formed from a 100 in. piece of steel.
To find the number of triangles that can be made from 100 inches of steel, divide 100 by the amount of steel needed for one triangle.
100  7 = 14 triangles
2 7
There is not enough steel to complete a fifteenth triangle. So the manufacturer can make 14 triangles from a 100 in. piece of steel.

58. Check It Out! Example 4b
Each measure is the side length of an equilateral triangle. Determine how many 10 in. triangles can be formed from a 100 in. piece of steel.
The amount of steel needed to make one triangle is equal to the perimeter P of the equilateral triangle.
P = 3(10)
P = 30 in.

59. Check It Out! Example 4b Continued
Each measure is the side length of an equilateral triangle. Determine how many 10 in. triangles can be formed from a 100 in. piece of steel.
To find the number of triangles that can be made from 100 inches of steel, divide 100 by the amount of steel needed for one triangle.
100  10 = 10 triangles
The manufacturer can make 10 triangles from a 100 in. piece of steel.

60. Homework (Choose 1 of the 3 options)
Make a set of flash cards. One card for each of the 7 triangles. Put an image and name of each triangle on one side and a description on the back.
List 7 real-world examples of where the 7 types of triangles can be seen. For example: Doritos® as equilateral triangles. (You cannot use mine )
Create a checklist of steps or things to check for when classifying triangles. For example: Step 1 – Examine the angle measures, etc.

61. Exit Slip In your brain, answer the following questions:
What did you learn today? Which of the 7 triangles is your favorite and why?