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I. Objectives: At the end of the lesson, students are expected to:
a. Name the largest and the smallest angle given
the sides of a triangle;
b. Arrange the sides of a triangle in order of
increasing length given the angles;
c. Cite ways to promote equality and prevent
inequalities.
II. Subject Matter: Theorems Involving Inequalities in a Triangle
Reference: Mathematics Learners’ Module Grade 8 page (350-353)
Skills: drawing, analyzing and solving
Values: disadvantage of inequalities
III. Materials: ruler, protractor, pintail pen, manila paper
IV. Procedure: 5A’s Method
Teacher’s Activity Students’ Activity
A. Awareness
a. Review
Good morning class!
(checking of attendance)
(checking of assignment)
What was our lesson last meeting?
What is again HyL Congruence Theorem?
How about the definition of HyA
Congruence Theorem?
Who can illustrate the HyL and HyA on the
board?
Very good!
Good morning Sir!
Our lesson last meeting was about
HyL and HyA Congruence
Theorem.
HyL Congruence Theorem states
that, “If the hypotenuse and a leg of
one right triangle are congruent to
the corresponding hypotenuse and a
leg of another triangle, then the
triangles are congruent”.
HyA Congruence Theorem states
that “If the hypotenuse and an acute
angle of one right triangle are
congruent to the corresponding
hypotenuse and an acute angle of
another right triangle, then the two
triangles are congruent”.
Student does as told
b. Motivation
In our previous discussions, we’ve
discussed about postulates and theorems of
congruence of triangles.
Now class, what if the sides and angles of a
triangle are not congruent, what do you
think?
Do you know class about certain theorems
of inequalities in a triangle?
c. Presentation
So be with me this morning as I discuss to
you about theorems involving inequalities
in a triangle.
d. Statement of the Aim
*name the largest angle and smallest angle
given the sides of a triangle;
*arrange the sides of a triangle in order of
increasing length given the angles;
*describe the disadvantage of inequality.
B. Activity
I will group in to two groups.
Let’s proceed to our activity.
Let one student to draw the figure on the
board
Let another student to explain the figure on
the board.
(possible answer)
No, Sir!
Theorems involving Inequalities in a
triangle
Student does as told
Student does as told
Do the following in your group;
1. Use a ruler to draw a triangle
named OPQ .
2. Make sure that OP is vertical
which measures 15cm, PQ is
horizontal which measures
20cm and OQ is diagonal
which measures 25cm.
3. Use a protractor to measure
the angles O, P and Q.
4. Indicate on the triangle OPQ
the measures of the three
sides and their opposite
angles
C. Analysis
What have observed about the sides of the
?OPQ
How are you going to describe the three
sides of ?OPQ
How about the angles then?
What is the shortest side?
What is the smallest angle?
Are the side OP and the angle Q
opposite?
So the smallest angle is opposite to the
shortest side.
What side is longer thanOP ?
What angle is greater than Q ?
Are the Q and PQ opposite?
Then, how are you going to describe the
longest side and the largest angles?
I observed that the sides and angles
of OPQ have different measures.
The three sides of OPQ are not
congruent.
The three angles also are not
congruent.
The shortest side isOP .
The smallest angle is Q ?
They are opposite because they are
facing each other.
The side which is longer than OP is
PQ ?
The angle which is greater than Q
is O .
They are opposite because they are
facing each other.
The largest side OQ and the largest
angle P are also opposite to each
other.
O
P Q
530
370950
20cm
15cm
25cm
D. Abstraction
How are you doing to conclude this
triangle OPQ in terms of the inequalities of
the sides and angles?
Another hand!
Very good!
For your better understanding, here are two
theorems which involve inequalities in a
triangle.
Everybody read and copy!
Values Integration
A while ago class we have discussed the
inequalities in a triangle.
Class, in connection to our real life
situation how are you going to promote
equality and to prevent inequality?
Exactly!
When the sides of a certain triangle
are not congruent then the angles
also are not congruent.
When the sides of a certain triangle
are not congruent then the opposite
angles of those sides are also not
congruent.
If two sides of a triangle are not
congruent, then the angles opposite
these two sides are not congruent,
and the larger angle is opposite the
longer side.
If two angles of a triangle are not
congruent, then the sides opposite
these two angles are not congruent,
and the longer side is opposite the
larger angle.
I can promote equality and prevent
inequality by being fair to
everybody in everything that I do.
Equality begins with being fair in
just a simple action. Just like falling
in line in a canteen, in withdraw
machine, or even in the bank, those
simple actions have great impacts on
the society since to promote equality
and at the same time to prevent
inequality among people.
E. Application
Activity 1
Directions: Name the largest and the
smallest angle of the
following triangles given the
length of sides.
1. In ABC , 12AB  , 16AC  and
19BC 
2. In DEF , 40DE  , 35DF  and
55FE 
3. In GHI , 32GI  , 50GH  and
35HI 
4. In JKL , 28JK  , 40KL  and
20JL 
5. In MNO , 22MN  , 38MO  and
50NO 
V. Evaluation
Directions: Arrange the sides of the
following triangles in the
order of increasing lengths
given the measures of angles.
1.
2.
,B A 
,D E 
,I H 
,J K 
,M O 
, ,ED RD RE
, ,ZY XY XZ
450
500
850
R
E
D
330
350
1150
X
Z
Y
3.
VI. Assignment
Directions: Fill the blanks with the correct
relation symbol (>,<) to show the
relationship: 1.) between segments, and 2.)
between angles in the corresponding
figures:
1. ___
2. ___
3. ___
4. ___
5. ___
In SON
m S m O
m S m N
m O m N
m N m O
m O m S

 
 
 
 
 
, ,LS DS DL
1.
2.
3.
4.
5.





450
600
750
D
L
S
O
S
N
25 45
56

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Theorems invloving inequalities in a triangle

  • 1. I. Objectives: At the end of the lesson, students are expected to: a. Name the largest and the smallest angle given the sides of a triangle; b. Arrange the sides of a triangle in order of increasing length given the angles; c. Cite ways to promote equality and prevent inequalities. II. Subject Matter: Theorems Involving Inequalities in a Triangle Reference: Mathematics Learners’ Module Grade 8 page (350-353) Skills: drawing, analyzing and solving Values: disadvantage of inequalities III. Materials: ruler, protractor, pintail pen, manila paper IV. Procedure: 5A’s Method Teacher’s Activity Students’ Activity A. Awareness a. Review Good morning class! (checking of attendance) (checking of assignment) What was our lesson last meeting? What is again HyL Congruence Theorem? How about the definition of HyA Congruence Theorem? Who can illustrate the HyL and HyA on the board? Very good! Good morning Sir! Our lesson last meeting was about HyL and HyA Congruence Theorem. HyL Congruence Theorem states that, “If the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and a leg of another triangle, then the triangles are congruent”. HyA Congruence Theorem states that “If the hypotenuse and an acute angle of one right triangle are congruent to the corresponding hypotenuse and an acute angle of another right triangle, then the two triangles are congruent”. Student does as told
  • 2. b. Motivation In our previous discussions, we’ve discussed about postulates and theorems of congruence of triangles. Now class, what if the sides and angles of a triangle are not congruent, what do you think? Do you know class about certain theorems of inequalities in a triangle? c. Presentation So be with me this morning as I discuss to you about theorems involving inequalities in a triangle. d. Statement of the Aim *name the largest angle and smallest angle given the sides of a triangle; *arrange the sides of a triangle in order of increasing length given the angles; *describe the disadvantage of inequality. B. Activity I will group in to two groups. Let’s proceed to our activity. Let one student to draw the figure on the board Let another student to explain the figure on the board. (possible answer) No, Sir! Theorems involving Inequalities in a triangle Student does as told Student does as told Do the following in your group; 1. Use a ruler to draw a triangle named OPQ . 2. Make sure that OP is vertical which measures 15cm, PQ is horizontal which measures 20cm and OQ is diagonal which measures 25cm. 3. Use a protractor to measure the angles O, P and Q. 4. Indicate on the triangle OPQ the measures of the three sides and their opposite angles
  • 3. C. Analysis What have observed about the sides of the ?OPQ How are you going to describe the three sides of ?OPQ How about the angles then? What is the shortest side? What is the smallest angle? Are the side OP and the angle Q opposite? So the smallest angle is opposite to the shortest side. What side is longer thanOP ? What angle is greater than Q ? Are the Q and PQ opposite? Then, how are you going to describe the longest side and the largest angles? I observed that the sides and angles of OPQ have different measures. The three sides of OPQ are not congruent. The three angles also are not congruent. The shortest side isOP . The smallest angle is Q ? They are opposite because they are facing each other. The side which is longer than OP is PQ ? The angle which is greater than Q is O . They are opposite because they are facing each other. The largest side OQ and the largest angle P are also opposite to each other. O P Q 530 370950 20cm 15cm 25cm
  • 4. D. Abstraction How are you doing to conclude this triangle OPQ in terms of the inequalities of the sides and angles? Another hand! Very good! For your better understanding, here are two theorems which involve inequalities in a triangle. Everybody read and copy! Values Integration A while ago class we have discussed the inequalities in a triangle. Class, in connection to our real life situation how are you going to promote equality and to prevent inequality? Exactly! When the sides of a certain triangle are not congruent then the angles also are not congruent. When the sides of a certain triangle are not congruent then the opposite angles of those sides are also not congruent. If two sides of a triangle are not congruent, then the angles opposite these two sides are not congruent, and the larger angle is opposite the longer side. If two angles of a triangle are not congruent, then the sides opposite these two angles are not congruent, and the longer side is opposite the larger angle. I can promote equality and prevent inequality by being fair to everybody in everything that I do. Equality begins with being fair in just a simple action. Just like falling in line in a canteen, in withdraw machine, or even in the bank, those simple actions have great impacts on the society since to promote equality and at the same time to prevent inequality among people.
  • 5. E. Application Activity 1 Directions: Name the largest and the smallest angle of the following triangles given the length of sides. 1. In ABC , 12AB  , 16AC  and 19BC  2. In DEF , 40DE  , 35DF  and 55FE  3. In GHI , 32GI  , 50GH  and 35HI  4. In JKL , 28JK  , 40KL  and 20JL  5. In MNO , 22MN  , 38MO  and 50NO  V. Evaluation Directions: Arrange the sides of the following triangles in the order of increasing lengths given the measures of angles. 1. 2. ,B A  ,D E  ,I H  ,J K  ,M O  , ,ED RD RE , ,ZY XY XZ 450 500 850 R E D 330 350 1150 X Z Y
  • 6. 3. VI. Assignment Directions: Fill the blanks with the correct relation symbol (>,<) to show the relationship: 1.) between segments, and 2.) between angles in the corresponding figures: 1. ___ 2. ___ 3. ___ 4. ___ 5. ___ In SON m S m O m S m N m O m N m N m O m O m S            , ,LS DS DL 1. 2. 3. 4. 5.      450 600 750 D L S O S N 25 45 56