1. A DETAILED LESSON PLAN IN MATHEMATICS FOR THIRD YEAR HIGH
SCHOOL
I. Learning Competencies
1. Identify the properties of parallelogram;
2. Apply the properties of parallelogram in problem solving;
3. Relate the properties of the parallelogram to the real world.
II. Subject Matter: Properties of Parallelogram
A. References
a. Textbook: Oronce, O.A & Mendoza, M. O. E-Math(Geometry).
2007. pages 238-243
B. Instructional Media
Visual Aids
C. Values Integration
• accuracy
• critical thinking
III. Learning Strategies
Teacher Activity Student Activity
A. Review
• What was our lesson last • Our previous lesson was all
meeting? about quadrilaterals.
• Very Good! What is a • A quadrilateral is any four-sided
parallelogram? figure which includes the
parallelogram, rhombus,
rectangle, trapezoid, and
square.
• Great!
B. Motivational Activity
• Do you want a game class? • Yes we do.
• Do you know the game trip to • Yes we do.
Jerusalem?
• Okay! The mechanics of the • Students follow.
game is that there are chairs
you are going to sit and one of
the chair has a cartolina which
has the consequence written
there and should do by the
person who can sit on that
certain chair when the music
stops.

2. C. Presentation
1. Student – Teacher Interaction
• Do you have an idea what our • Our lesson for today is all about
lesson is for today? properties of parallelogram.
• Precisely! But first, what is a • A parallelogram is a
parallelogram? quadrilateral having 2 pairs of
parallel lines.
• Exactly! A parallelogram is a • Students follow
quadrilateral with both pairs of
opposite sides parallel. Consider
this parallelogram ABCD, ĀB
and CD parallel to each other
(AB // CD) and if segments AD
and BC are also parallel to each
other (AD // BC), then the
quadrilateral is a parallelogram.
• Now, may I call on Mary Chris to • Student does so.
draw a line segment AC.
• What do you call this segment in • Maam, that is a diagonal.
terms of parallelogram?
• In this illustration, we have the • Students follow.
first property which states, “Each
diagonal of a parallelogram
divides the parallelogram into
two congruent triangles.” The
following is the proof of this
property.
A B
DC
Given: □ABCD
AC is a diagonal.
Prove: ∆ABC is congruent to ∆CDA
Proof:

3. Statements Reasons
1. □ABCD is a 1. Given.
parallelogram.
2. AB // DC, 2. Definition of
AD // BC
parallelogram.
3. angle 1 is 3. The PAIA
Congruent to theorem
Angle 2
4. angle 3 is 4. The PAIA
congruent to Theorem
angle 4
5. AC is 5. Reflexive
congruent to property
AC
6. ∆ABC is 6. ASA
Congruent to Postulate
∆CDA
• Students follow.
• nd
Then the 2 property is that,
opposite sides of a
parallelogram are congruent. • From the 1st property, I can say
• From the illustration of AB is congruent to DC and AD is
parallelogram ABCD where congruent to BC by CPCTC
∆ABC is congruent to ∆ADC, (congruent parts of a congruent
which sides are congruent? triangle are congruent).
Why? • From the 1st property also, I can
• Brilliant! Next the 3rd property is: say angle B is congruent to
opposite angles of a angle D by CPCTC. If diagonal
parallelogram are congruent. BC is used, then angle A is
Which angles are congruent? congruent to angle Cm also by
Why? CPCTC.
• Angle A and angle B are
• Yeah! You’re correct! After that supplementary since they are
the 4th property is that any two consecutive angles of
consecutive angles of a parallelogram ABCD which are
parallelogram are interior angles on the line
supplementary. As we observed segment AB transversal.
on the parallelogram ABCD, line
segment BC // line segment AD
and line segment AB is a
transversal. What can you
conclude about angle A and
angle B?
• Angle C ands angle D is also

4. • Magnificent! Now, how about if supplementary since they’re
line segment CD is the consecutive angles of
transversal, what can you parallelogram ABCD which are
conclude about angle C and interior angles on the line
angle D? segment AB transversal.
• Students follow.
• Amazing you’re so brilliant
students! And finally, we have
the last property which states,
“The diagonals of a
parallelogram bisect each • Students follow.
other.”
• As a proof of this property
consider this parallelogram
ABCD.
A 1 B
4
Q
3
2
D C
Given: □ABCD is a parallelogram.
Line segment AC and line
segment BD are the
diagonals.
Prove: Line segment AQ is
congruent to line segment
CQ.
Line segment BQ is
congruent to line segment
DQ.
Proof:
Statements Reasons
1. □ABCD is a 1. Given.
parallelogram.
2. Line segment AB 2. Definition
of
// line segment DC
parallelogram
3. Angle 1 is 3. The PAIC
congruent to Theorem

5. angle 2, angle 3
is congruent to
angle 4.
4. Line segment AB 4. Opposite
is congruent to sides of a
line segment BC
parallelogram
5. ∆ABQ is 5. ASA
congruent to Postulate
∆CDQ
6. Line segment AQ 6. CPCTC.
Is congruent to
line segment CQ,
line segment BQ • 1,2,3,1,…..
is congruent to
line segment DQ • Students dos so.
2. Synthesis • Students do so.
• As an activity, please count
off, 1-3 start on you.
• Group 1 stay here , 2 on that
area, & 3 on the last row.
• In your group choose your • C A
facilitator, secretary and
rapporteur. Then the facilitator
will come here and get your
problem.
• Finished? Are you done?
Group 1 will be the first to
report and so on. Okay! Let’s
hear from group 1. E R
Use the figure at the right to answer the
following:
a. What triangles of parallelogram
CARE is congruent?
Answer: ∆CRE and ∆RCA.
b. Which sides of parallelogram CARE
are congruent?
Answer: Angle C and angle R, Angle
A and angle E.
• Given: □ELOG is a
parallelogram.
EL = 5x -5 and
GO = 4x+1.

6. Find EL.
• Very Good! Let us hear from
group 2.
E L
G O
Solution:
Use definition of parallelogram.
EL = GO
5x-5 = 4x+1
X=6
Thus, EL = 5(6)-5 = 25
• In the figure, □LEOG is a
parallelogram, LO = 34.8 and
m<EOG=72. Find LR and
m<LGO.
L E
• Wow! Group 3?
R
G O
Solution:
The diagonals of a parallelogram bisect
each other line segment LO and line
segment GE is diagonals.
Consecutive angles of a parallelogram
are supplementary. Angle EOG and
angle LGO are consecutive angles,

7. m<LGO=180-72+108.
3. Generalization
To summarize, the ff. are the
properties of a parallelogram.
A B
P
D C
1. Opposite sides are congruent.
 Line segment AB is
congruent to line
segment CD, Line
segment AD is
congruent to line
segment CB
2. Opposite angles are congruent
 Angle A is congruent to
angle C, Angle B is
congruent to angle D
3. Any two consecutive angles are
Supplementary.
 Angle A & angle B are
supplementary.
 Angle B & angle C are
supplementary
 Angle C & angle D are
supplementary
 Angle A and angle D are
supplementary
4. Diagonals bisect each other.
 Line segment AP is
congruent to line segment
CP, line segment BP is

8. congruent to line segment
DP
IV. Evaluation
A. Answer the ff. by referring to the figure.
Given: □SURE is a parallelogram.
R
E
D
T
U
S
U
1. If Su = 7, then RE = _________
2. ∆SUE = _________
3. ∆SUR = _______
4. UT = _________
5. ST = _________
6. If SE = 12, then RU=________
7. Angle U = ________
8. Angle S = ________
9. SU = ______
10. If m<S=73, then m<R=_____
11. If m<E=75, then m<R=________
12. If m<U=95, then m<E=_______
13. m<S+m<E=________
14. If m<S=60, then m<_______=60

9. 15. If m<URS-55, m<ESR=________
V. Assignment
A. Use the properties of a parallelogram to do what is asked.
B A □BATH is a parallelogram.
H T
S
1. Given: BH = 7x-10
AT = 4x-1
Find: BH=_________
2. Given: HS=10x+7
AS=5x+22
Find: HA
Prepared by:
Anjelyn Betalas
BSE Mathematics III

10. 15. If m<URS-55, m<ESR=________
V. Assignment
A. Use the properties of a parallelogram to do what is asked.
B A □BATH is a parallelogram.
H T
S
1. Given: BH = 7x-10
AT = 4x-1
Find: BH=_________
2. Given: HS=10x+7
AS=5x+22
Find: HA
Prepared by:
Anjelyn Betalas
BSE Mathematics III

11. 15. If m<URS-55, m<ESR=________
V. Assignment
A. Use the properties of a parallelogram to do what is asked.
B A □BATH is a parallelogram.
H T
S
1. Given: BH = 7x-10
AT = 4x-1
Find: BH=_________
2. Given: HS=10x+7
AS=5x+22
Find: HA
Prepared by:
Anjelyn Betalas
BSE Mathematics III