1. 5.1 Classifying Triangles
SWBAT classify triangles in the coordinate plane

2. Classification means put things into a group according to how they are alike.

3. We will break this group of animals into smaller groups.

4. Can't Fly
Can Fly
The same animals can be put into different groups depending on what we look at when we classify them.
Extinct
Still Living

5. Today you will learn how triangles can be classified in two different ways...

6. Think of all the different kinds of triangles you know.
Did you come up with all of these?
Acute Obtuse Right
Scalene Isosceles Equilateral

7. Triangle The three endpoints are called vertices.
A polygon with 3 sides.
The three endpoints are called vertices.

8. Classifying by side lengths
Isosceles
at least two
Scalene
none
Equilateral
all 3

9. Scalene Triangle
All sides are different lengths.

10. Isosceles Triangle
At least two out of the three sides are equal lengths.

11. Equilateral Triangle
All sides have the same length

12. Classify this triangle by its sides.
ISOSCELES

13. Classify this triangle by its sides.
SCALENE

14. Classify this triangle by its sides.
EQUILATERAL

15. Classify the following triangles by their sides. Use these signals:
Scalene
Isosceles
Equilateral

16. Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

17. Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

18. Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

19. What formula do you use to determine if a triangle is scalene, isosceles, or equilateral?
Answer: The terms scalene, isosceles, and equilateral have to do with side lengths of a triangle so you use the Distance Formula.

20. Classifying by angle measures
Acute
acute
right
Right
Obtuse
obtuse

21. Acute Triangle
All three angles are less than 900.
800
400
600

22. Obtuse Triangle
One of the three angles is more than 900
200
300
1300

23. Right Triangle
One of the three angles is exactly 900

24. Classify the following triangles by their sides. Use these signals:
Acute
Obtuse
Right

25. Classify by angles.
Acute
Obtuse
Right

26. Classify by angles.
1000
Acute
Obtuse
Right

27. Classify by angles.
850
450
500
Acute
Obtuse
Right

28. A B C D E
Now you should be able to classify any triangle by both its side lengths and its angles.

29. Classify the triangles by sides lengths and angles
a) b) c) 7
40°
15° 25 24
70°
70°
120°
45°
Solutions:
Scalene, Right
Isosceles, Acute
Scalene, Obtuse

30. Classify a triangle in a coordinate plane
Example 1
Classify a triangle in a coordinate plane
Determine whether PQO with vertices at P(-1, 2), Q(6, 3), O(0, 0), is scalene, isosceles, or equilateral. Explain.
SOLUTION
Use the distance formula to find the side lengths. OP = y 2 – 1 ( ) x + = 2 – ( )
(– 1 ) + 5
2.2 OQ = y 2 – 1 ( ) x + 2 = – ( ) 6 + 3 45
6.7 PQ = y 2 – 1 ( ) x + 3 – 2 ( ) 6 + =
(– 1 ) 50
7.1

31. EXAMPLE
Classify a triangle in a coordinate plane (continued)
PQO is a scalene triangle since none of the sides are congruent.
Explanation
Determine whether PQO with vertices at P(-1, 2), Q(6, 3), O(0, 0), is scalene, isosceles, or equilateral. Explain.

32. c. equilateral triangles
Ex: Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, BCE, BDE, CDE, ACD, ABD
c. equilateral triangles
Answer: None!
Example 1-2c

33. Exit Slip
Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain.
Answer:
AB = 5
BC = 5
CA = 7.1
Since AB = Triangle ABC is isosceles since two of the sides are congruent.

34. Triangle Sum Theorem x + y + z = 180 x y z
The sum of the measures of the angles of a triangle is 180°
x + y + z = 180 x y z

35. Find the missing angles.1) 2) y
31°
26°
65°
35° x 3)
30° x° y°
70° 4) y° x°
41°
82° z° 80
2) 123
3) x = 60, y = 30
4) x = 57, y = 57, z = 82

36. Example:
The measures of the angles of a triangle are in the ratio 1:3:5. Find the measure of each angle.
x + 3x + 4x = 180
8x = 180
x = 22.5 3x
Plug in to find each angle:
1(22.5)= 22.5°
3(22.5) = 67.5°
4(22.5) = 90° x 4x