Quadrilaterals

1. Classroom Observation No. 1
Grade 9 Mathematics
ARGEL P. DALWAMPO
SST-1 Math
GEOMETRY

2. OPENING
PRAYER

3. What I need to
Know?
As you go through this lesson, think of these important
questions:
 “How to illustrate the measure of sides and
angles of polygons?
 “What is the importance of knowing the
different properties of parallelogram?

4. Four-Sided Everywhere!
What’s new?

5. Questions:
1. What do you see in the previous
illustrations?
2. Do you see parts that show quadrilaterals?
3. Can you give some significance of their
designs?
4. What might happen if you change their
designs?
5. Can you give other things around you whose
shape/ parts must be a parallelogram?

6. Review:
A. Name the following parts of
quadrilateral VIRA.
1. Opposite sides
2. Opposite angles
3. Consecutive angles
4. Diagonals
5. Triangles formed by a diagonal
B. Name me. I am this quadrilateral
made from two pairs of
intersecting parallel lines. Who am
I?
A A A E G L L L M O P R R

7. Learning Task 1- Fantastic Four!
Materials: protractor, graphing paper, ruler, pencil, and
compass
Procedures:
1. Draw a parallelogram OBEY on graphing paper.
2. Measure the sides and the angles, and record your
findings in your own table similar to what is shown
below.
3. Draw the diagonals and measure the segments
formed by the intersecting diagonals. Record your
findings in the table.

8. In your drawing, identify the
following:
Measurements Are the measurements
equal or not equal?
Pairs of opposite sides
Pairs of opposite
angles
Pairs of consecutive
angles
Pairs of segments
formed by intersecting
diagonals
4. Make a conjecture on the following measures:
a. slope of opposite sides
b. lengths of opposite sides
c. measures of opposite angles
d. measures of consecutive angles
e. diagonals

9. Properties of Parallelogram
1. In a parallelogram, any two opposite sides are congruent.
2. In a parallelogram, any two opposite angles are congruent.
3. In a parallelogram, any two consecutive angles are
supplementary.
4. The diagonals of a parallelogram bisect each other.
5. A diagonal of a parallelogram forms two congruent triangles.

10. 1. The opposite sides are parallel. 𝐴𝐵//𝐷𝐶 𝑎𝑛𝑑 𝐴𝐷//𝐵𝐶
2. The opposite sides are congruent. 𝐴𝐵 ≅ 𝐷𝐶 𝑎𝑛𝑑 𝐴𝐷 ≅ 𝐵𝐶
3. The opposite angles are congruent. ∠𝐴 ≅ ∠𝐶 𝑎𝑛𝑑 ∠𝐵 ≅ ∠𝐷
4. The consecutive angles are supplementary.
𝑚∠𝐴 + 𝑚∠𝐵 = 180° 𝑚∠𝐵 + 𝑚∠𝐶 = 180°
𝑚∠𝐶 + 𝑚∠𝐷 = 180° 𝑚∠𝐴 + 𝑚∠𝐷 = 180°
5. The diagonals bisect each other.
Diagonal 𝐴𝐶 bisects 𝐵𝐷,
this means 𝐵𝐸 ≅ 𝐷𝐸
Diagonal 𝐵𝐷 bisects 𝐴𝐶,
his means 𝐴𝐸 ≅ 𝐶𝐸
5. Each diagonal bisects the parallelogram into two congruent triangles.
For diagonal 𝐴𝐶, ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
For diagonal 𝐵𝐷, ∆𝐵𝐶𝐷 ≅ ∆𝐷𝐴𝐵
EXAMPLE NO. 1

11. EXAMPLE NO. 2
Use the properties
of parallelogram to
solve the missing
measures of angles/
sides.
Angle/Side Measure
∠𝐴𝐸𝐺
∠𝐸𝐺𝑅
∠𝐺𝑅𝐴
∠𝑅𝐴𝐸
𝐺𝐸
𝐸𝐴
25 cm
20 cm
𝟏𝟐𝟎°
6𝟎°
𝟏𝟐𝟎°
6𝟎°
𝟐𝟓 𝒄𝒎
𝟐𝟎 𝒄𝒎

12. What I have learned
Choose the letter of the correct answer. Use the properties of parallelogram to
solve the following. Refer to parallelogram COVD below.
1. The side congruent to 𝐷𝑉.
a. 𝐷𝑂 b. 𝐶𝐷 c. 𝐶𝑂 d. 𝐶𝑉
2. The angle congruent to ∠𝐶𝑂𝑉.
a. ∠𝐶𝐷𝑉 b. ∠𝐷𝐶𝑂 c. ∠𝐷𝑉𝑂 d.∠𝑂𝐶𝑉
3. The congruent line segments when 𝐶𝑉𝑏𝑖𝑠𝑒𝑐𝑡𝑠 𝑂𝐷
a. 𝐶𝑂 𝑎𝑛𝑑 𝑂𝑉 c. 𝑂𝐼 𝑎𝑛𝑑 𝐷𝐼
b. 𝐶𝐷 𝑎𝑛𝑑 𝐷𝑉 d. 𝐶𝑉 𝑎𝑛𝑑 𝑂𝐷
4. The angle supplementary to ∠𝐶𝐷𝑉
a. ∠𝐶𝐷𝑂 b. ∠𝑂𝐷𝑉 c. ∠𝐶𝑂𝑉 d. ∠𝐷𝑉𝑂
5. The two congruent triangles formed by diagonal 𝐷𝑂
a. ∆𝐷𝐶𝑂 𝑎𝑛𝑑 ∆𝑂𝑉𝐷 c. ∆𝐶𝐼𝑂 𝑎𝑛𝑑 ∆𝑉𝐼𝐷
b. ∆𝐶𝑂𝑉 𝑎𝑛𝑑 ∆𝑉𝐷𝐶 d. ∆𝐶𝐼𝐷 𝑎𝑛𝑑 ∆𝑉𝐼𝑂

13. 6. If 𝑚∠𝐶𝑂𝑉 = 750, find 𝑚∠𝑂𝐶𝐷
a. 750
b. 950
c. 1050
d. 1800
7. What is the length of 𝐶𝑂 if 𝐷𝑉 = 25 𝑐𝑚?
a. 12.5 cm b. 25 cm c. 50 cm d. 100 cm
8. If 𝐶𝑉 = 30 𝑐𝑚, find 𝐶𝐼
a. 60 cm b. 40 cm c. 30 cm d. 15 cm
9. If 𝑂𝐷 is 6 more than 𝐶𝑉, and 𝐶𝐼 = 9, then 𝐷𝐼 =_______
a. 6 cm b. 9 cm c. 12 cm d. 24 cm
10. Your father is about to enclose your garden with barbed wires. Its shape is like
parallelogram COVD above. He asked you about the total length of barbed
wires needed if CO is twice as long as OV and CD=8 m.
a. 48 m b. 32 m c. 16 m d. 8 m

14. What I Can Do (Fantastic Parallelogram!)
Materials: measuring tools like ruler and protractor, any
objects at home (old magazines, brochures, newpapers),
scissors, paste/glue, oslo paper.
Procedures:
1. Create a collage of objects that are quadrilaterals.
2. From any of the pictures, select at most 3 objects that can
be seen at your surroundings.
3. Measure its parts so as to prove that that is a
parallelogram.
4. Write your findings in the oslo paper.
5. Then, write at least 2 to 3 sentences about what you have
learned from the lesson.

15. Criteria Outstanding (4) Satisfactory (3) Developing (2) Beginning (1)
Accuracy Measurements are
accurate and show
wise use of the key
concepts in the
properties of
parallelograms
Measurements are
accurate and show
use of the key
concepts in the
properties of
parallelograms
Measurements are
erroneous and show
some use of the key
concepts in the
properties of
parallelograms
Measurements are
erroneous and do not
show the use of the key
concepts in the
properties of
parallelograms
Mathematical
Justification
The explanations and
reasoning are very
clear, precise and
coherent. It included
facts and principles
related to
parallelograms.
The explanations
and reasoning are
clear, precise and
coherent. It
included facts and
principles related to
parallelograms.
The explanations and
reasoning are vague
but it included facts
and principles related
to parallelograms.
The explanations and
reasoning are vague and
it didn’t include facts
and principles related to
parallelograms.
Creativity The overall impact of
the output is very
impressive.
The overall impact
of the output is
impressive.
The overall impact of
the output is fair.
The overall impact of
the output is poor
Rubrics

16. THANK YOU
GODBLESS