Describe an arithmetic sequence. Find the nth term of an arithmetic sequence. Appreciate arithmetic sequence in solving real life problems.

1. Mathematics
8
4th
Quarter
WELCOME to

2. Activity:
Loop-A-Word
Lesson 1

4. At the end of the lesson, the learners will be
able to;
• State the theorem on triangle inequalities,
exterior angle inequality, and hinge theorem;
• Illustrate the theorem on triangle inequalities,
exterior angle inequality, and hinge theorem; and
• Develop positive attitude towards work.

5. Inequality in Triangles
Let’s Discuss!

6. Illustrative Example 1:
Observe the given
figure on the right.

7. Exterior Angle of a Triangle
An exterior angle of a triangle is an angle that
forms a linear pair with an interior angle of a
triangle is extended.

8. Illustrative Example 2:
Observe the given
figure on the right.

9. Triangle Inequality Postulate
The length of a side of a triangle is less than
the sum of the lengths of the other two sides.
The length of one side is also greater than the
positive difference of the lengths of the other
two sides.

10. Illustrative Example 3:
Observe the given
figure on the right.

11. Theorem:
If the length of the two sides of a triangle is
unequal, the measures of the angles are also
unequal. The longer side is opposite the angle
with a greater measure.

12. Illustrative Example 4:
Observe the given
figure on the right.

13. Hinge Theorem
If two sides of a triangle are congruent to the
sides of another triangle, but their included
angles are not, then the remaining sides are
unequal. The longer side is opposite of the
larger angle.

14. Guided Practice:
Try This!
Lesson 1

15. Direction: Fill the blanks with the correct
relation symbol ( >, < ) to show the relationship.

16. Direction: Fill the blanks with the correct
relation symbol ( >, < ) to show the relationship.

17. Direction: Fill the blanks with the correct
relation symbol ( >, < ) to show the relationship.

19. Direction: Fill the blanks with the correct
relation symbol ( >, < ) to show the relationship.

20. Seatwork #1
Lesson 1

25. Inequality in Triangles
Let’s Discuss!

30. Let’s Analyze!
Guided Practice

32. Seatwork #4:
Copy and
Answer on
your Quiz
notebook FU

33. FU

34. FU

35. FU

36. FU

37. Let’s Review!

38. Which of the following are the remote interior
angles of ∠3 in figure 6?
A. ∠1 and ∠2
B. ∠2 and ∠4
C. ∠4 and ∠5
D. 5 and 6
∠ ∠
Figure 6

39. David Wayne interpeted the given figure below.
He proved that . Which is NOT part of his
proof?
A. Linear Pair
B. Reflexive Property
C. Hinge Theorem
D. Converse of the Hinge Theorem

40. Study the figure below. Which of the following
should be the correct conclusion using the
converse of the hinge theorem?
A.
B.
C.
D.

41. Properties of
Parallel Lines
Cut by a
Transversal
Lesson 3

42. If in the given figure x║y, z is a transversal, by the
postulate mentioned above , we can conclude the
following: