1. 5-1 Classifying Triangles
Geometry

2. Today we will be learning how to classify triangles according to length of sides and measurement of the angles.

3. First we will learn to classify by the
ANGLES

4. Right triangles have ONE right angle

5. Acute Triangles have three acute angles
Smaller than 90o
Smaller than 90o
Smaller than 90o

6. Obtuse Triangles have ONE obtuse angle

7. We will now learn to classify triangles by their sides.

8. Equilateral Triangles have 3 equal sides
If you collapsed all of the sides they would form a line.

9. Isosceles Triangles have 2 equal sides.

10. Scalene Triangles have NO equal sides.

11. Classifying Triangles by Their Sides
EQUILATERAL – 3 congruent sides
ISOSCELES – at least two sides
congruent
SCALENE – no sides congruent
EQUILATERAL
ISOSCELES
SCALENE

12. Classifying Triangles by Their Angles
EQUIANGULAR – all angles are congruent
ACUTE – all angles are acute
RIGHT – one right angle
OBTUSE – one obtuse angle
ACUTE
EQUIANGULAR
RIGHT
OBTUSE

13. Can You Classify the Different Triangles in the Picture Below?
Classify the following triangles: AED, ABC, ACD, ACE
Triangle AED = Equilateral, Equiangular
Triangle ABC = Equilateral, Equiangular
Triangle ACD = Isosceles, Obtuse
Triangle ACE = Scalene, Right

14. 1-1a

15. Slide 3 of 3
1-3a

16. Slide 3 of 3
1-3b

17. Slide 3 of 3
1-3c

18. Slide 3 of 3
1-3d

19. You have now learned that triangles can be classified by either their sides or their angles.

20. 5-2 Angles of a Triangle

21. Slide 1 of 2
1-1a

22. Slide 2 of 2
1-2a

23. Slide 2 of 2
1-2b

24. Slide 2 of 2
1-2c

25. Slide 2 of 2
1-2d

26. Slide 2 of 2
1-2d

27. Slide 2 of 2
1-2e

28. Slide 2 of 2
1-2e

29. Slide 2 of 2
1-2f

30. Slide 2 of 2
1-2g

31. Slide 2 of 2
1-2h

32. Slide 2 of 2
1-2i

33. Slide 2 of 2
1-2j

34. Slide 2 of 2
1-2j

35. Write and solve an equation to find the value of x.
EXAMPLE 3
Find an angle measure
Find m∠ JKM.
SOLUTION
STEP 1
Write and solve an equation to find the value of x.
(2x – 5)° =
70° + x°
Apply the Exterior Angle Theorem.
x = 75
Solve for x.
STEP 2
Substitute 75 for x in 2x – 5 to find m∠ JKM.
2x – 5 = 2 75
– 5 =
145
The measure of ∠ JKM is 145°.
ANSWER

36. GUIDED PRACTICE
for Examples 3 and 4
Find the measure of 1 in the diagram shown.
The measure of ∠ 1 in the diagram is 65°.
ANSWER

37. GUIDED PRACTICE
for Examples 3 and 4 x 2x 3x
Find the measure of each interior angle of ABC, where m A = x , m B = 2x° , and m C = 3x°.
SOLUTION
A + B C =
180°
x + 2x + 3x =
180°
6x =
180°
x =
30°
B =
2x =
2(30) =
60°
C =
3x =
3(30) =
90°

38. GUIDED PRACTICE
for Examples 3 and 4
Find the measures of the acute angles of the right triangle in the diagram shown.
26° and 64°
ANSWER