INEQUALITIES IN A TRIANGLE angle relationship.pptx

1. INEQUALITIES IN A TRIANGLE
(Relationship Among Angles of a Triangle)
EXTERIOR ANGLE EQUALITY THEOREM
EXTERIOR ANGLE INEQUALITY THEOREM

2. DIFFERENT ANGLES IN A TRIANGLE
1.INTERIOR ANGLE
 is an angle inside the triangle.

3. DIFFERENT ANGLES IN A TRIANGLE
2. EXTERIOR ANGLE
 is an angle which is adjacent and
supplementary to one of the
angles of the triangle.

4. DIFFERENT ANGLES IN A TRIANGLE
3. REMOTE INTERIOR ANGLE
 angles which are not adjacent to
the given exterior angle of the
triangle.

5. DIFFERENT ANGLES IN A TRIANGLE
4. ADJACENT INTERIOR ANGLE
 is an interior angle which forms
a linear pair with the given
exterior angle.

6. DIFFERENT ANGLES IN A TRIANGLE
Interior Angles
Exterior Angles
Remote Interior Angles
Adjacent Interior Angles

7. Relations Among Angles of a Triangle
EXTERIOR ANGLE EQUALITY THEOREM
 The measure of an exterior
angle is equal to the sum of its
remote interior angles.

8. EXTERIOR ANGLE EQUALITY THEOREM
Exterior Angles
Remote Interior Angles

9. EXTERIOR ANGLE EQUALITY THEOREM
Exterior Angles
Remote Interior Angles

10. EXTERIOR ANGLE EQUALITY THEOREM
Exterior Angles
Remote Interior Angles

11. Relations Among Angles of a Triangle
EXTERIOR ANGLE INEQUALITY THEOREM
 The measure of an exterior
angle of a triangle is greater than
the measure of either of the two
remote interior angles.

12. EXTERIOR ANGLE EQUALITY THEOREM
Exterior Angles
Remote Interior Angles

13. EXTERIOR ANGLE EQUALITY THEOREM
Exterior Angles
Remote Interior Angles

14. EXTERIOR ANGLE EQUALITY THEOREM
Exterior Angles
Remote Interior Angles

15. EXERCISES:
1. Name each of
the exterior
angles in the
figure?

16. ANSWER
1. EXTERIOR ANGLES

17. EXERCISES:
2. Name each
of the
interior
angles in the
figure?

18. ANSWER
2. INTERIOR ANGLES

19. EXERCISES:
3. Which are
the remote
interior
angles of
exterior
angle QON?

20. EXERCISES:
3. REMOTE INTERIOR
ANGLES OF ∠𝑸𝑶𝑵?

21. EXERCISES:
4. Which are
the remote
interior
angles of
exterior
angle PMO?

22. ANSWER
4. REMOTE INTERIOR
ANGLES OF ∠𝑷𝑴𝑶?

23. EXERCISES:
5. Which are
the remote
interior
angles of
exterior
angle RNM?

24. ANSWER
5. REMOTE INTERIOR
ANGLES OF ∠𝑹𝑵𝑴?

25. FINDING VALUES OF UNKNOWN ANGLE.
6. If m∠𝟏 = 𝟏𝟑𝟐 𝐚𝐧𝐝 𝐦∠𝟑 = 𝟖𝟓, 𝒇𝒊𝒏𝒅 𝒎∠𝟒.

26. FINDING VALUES OF UNKNOWN ANGLE.
6. If m∠𝟏 = 𝟏𝟑𝟐 𝐚𝐧𝐝 𝐦∠𝟑 = 𝟖𝟓, 𝒇𝒊𝒏𝒅 𝒎∠𝟒.

27. FINDING VALUES OF UNKNOWN ANGLE.
7. If m∠𝟑 = 𝟗𝟓 𝐚𝐧𝐝 𝐦∠𝟒 = 𝟑𝟓, 𝒇𝒊𝒏𝒅 𝒎∠𝟏.

28. FINDING VALUES OF UNKNOWN ANGLE.
7. If m∠𝟑 = 𝟗𝟓 𝐚𝐧𝐝 𝐦∠𝟒 = 𝟑𝟓, 𝒇𝒊𝒏𝒅 𝒎∠𝟏.

29. FIND THE VALUE OF X IN EACH OF THE FOLLOWING:

30. FIND THE VALUE OF X IN EACH OF THE FOLLOWING:

31. FIND THE VALUE OF X IN EACH OF THE FOLLOWING:

32. THANK YOU FOR LISTENING!!!