The document discusses applying theorems on triangle inequalities. It involves: 1) Recalling the Hinge theorem and its converse to compare triangle inequality statements. 2) Applying triangle inequality theorems to compare statements of inequalities. 3) Displaying appreciation for the lesson by answering exercises.

1. COMPETENCY: Applies theorems on
triangle inequalities (M8GE-Ivb-1)
A.Recall Hinge theorem and the Converse of
Hinge;
B.Applies theorems of triangle inequalities to
compare statements of inequalities;
C.Display appreciation of the lesson by
actively answering the exercises given.

2. Using the Hinge Theorem and its
Converse, complete with <, > or =.
RS ____ TU 2. m∠1 ____ m∠2 3.
m∠1 ____ m∠2 4. AB ____ CB

5. I N E
U
L
C D

6. O P T
S
O
P I E

7. A N E
L
G S

8. T H R
I D

9. E Q A
U L

10. P A T
R S

12. Is larger.
o
f

13. In learning, age, gender
and race DON’T matter!
A car jack is used to lift a car. The
jack shown below is one of the
simplest still in use today

14. What have you noticed with
the following as the jack is
lowered?
1. legs of the isosceles
∆ABC
2. the included ∠A?
3. the side opposite ∠A?

15. If the two sides of a
triangle are congruent
to two sides of another
triangle and the
included angle of the
first is larger than the

16. Let the students answer the
following items by group:
Group 1. Illustration

17. You and your friend are flying separate
planes. You leave the airport and fly 120
miles due west. You then change direction
and fly W 300 N for 70 miles. (W 300 N
indicates a north-west direction that is 300
north of due west.) Your friend leaves the
airport and flies 120 miles due east. She
then changes direction and flies E 400 S
for 70 miles. Each of you has flown 190
miles, but which plane is farther from the
airport?

18. GROUP 2 Explanation
The position of the
swings changes based on
how hard the swing is
pushed.
Which pairs of segments
are congruent?

19. GROUP 3. LOCKERS
Illustrate and explain
Neva and Shawn both have
their lockers open as shown
in the diagram. Whose locker
forms a larger angle? Explain
your reasoning.

20. Group 4. Solving with explanation
Fill the box with >, <, or = htm2

21. Multi-step Problem Use the diagram of the tank
cleaning system’s expandable arm shown below.
A. As the cleaning system arm expands,
𝐸𝐷 gets longer. As 𝐸𝐷 increases, what
happens to m∠EBD? What happens to
m∠DBA?
B. Name a distance that decreases as ED
gets longer

22. The teacher summarizes the mathematical
skills or principles used to recognize the
triangle inequality theorems and apply it in
real life.
1. What did you do to arrive at the answer?
2. Where there mathematical skills or
principles used in recognizing Hinge and its
converse theorem?

23. A. CRANES
In the diagram, a crane is
shown lifting an object to two
different heights. The length
of the red arm of the crane is
fixed. Which is shorter MN or
RS?
Explain your reasoning.

24. B. Write an inequality, or set of inequalities,
to describe the possible values for x