The document outlines the properties and identification criteria for different types of parallelograms. It includes activities to help determine if a quadrilateral is a parallelogram based on congruent sides, angles, and diagonals. Additionally, it provides exercises for calculating various measurements within parallelograms, as well as real-world applications related to farming.

1. QUADRILATERALS
THAT ARE
PARALLELOGRAM

2. ACTIVITY 1: REFRESH YOUR MIND
KIND FIGURE DEFINITION
Quadrilateral
Parallelogram
Rectangle
Rhombus
Square
Kite

3. Aparallelogramwith
four right angles
A quadrilateral with two
distinctpairsofadjacent,
congruent sides
Aquadrilateralwithtwo
pairs of opposite sides
parallel
Closed plane figure
consistingoffourline
segments or sides
Aparallelogramwithall
four sides congruent
Arectanglewithallfour
sides congruent

4. 1. Which among the
quadrilaterals above are
parallelogram?
2. How can you identify that a
quadrilateral is a
parallelogram?

5. Identify
the
following:
Segments
/ Angles
measure
ment
Are the
measurements equal
or not?
Pair of
opposite
sides
Pairs of
opposite
angles

6. PROPERTY NO. 1
In a parallelogram,
any two opposite
sides are congruent

7. PROPERTY NO. 1
Example:
Given quadrilateral ABCD, if 𝑨𝑩 ≅ 𝑪𝑫 and
𝑩𝑪 ≅ 𝑨𝑫, then quadrilateral ABCD is a
parallelogram. B
D
A
C
6 cm
6 cm
4 cm
4 cm

8. PROPERTY NO. 1
In a parallelogram,
any two opposite
angles are congruent

9. PROPERTY NO. 2
Example:
Given quadrilateral ABCD, if∠𝐴 ≅ ∠𝐶 and∠𝐵 ≅ ∠𝐷,
then quadrilateral ABCD is a parallelogram.
B
D
A
C
115°
115°
65°
65°

10. ACTIVITY NO. 3 : PLOT, CONNECT, IDENTIFY
1. P(-2,-1) ; L(-2,2); O(1,2); T(1,-1)
2. W(-4,-4) ; O(-4,-2); R(0,-2); D(0,-4)
3. L(-5,-1); E(-3,3); A(2,3); P(0,-1)
4. C(0,1); O(3,5); N(6,1); E(3,-3)
5. K(-4, -4); N(-2,0); O(2, 0); W(4, -4)
6. B(-2, 0); O(0, 3); R(2,0); N(0,-6)

11. A rectangular lot ABCD has a length of 12 cm
and a width of 7 cm as shown in the figure
below.
B
D
A
C
12 cm
12 cm
7 cm 7 cm

12. What are the different kinds of
quadrilaterals that are parallelograms?
How can you identify whether a
quadrilateral is a parallelogram?
In a parallelogram?

13. MODIFIED TRUE OR FALSE
Consider parallelogram NOTE below. Write true if the statement is correct,
otherwise change the underlined term/word to make the statement correct.
1. ̅𝑁̅̅𝐸̅ is congruent to ̅𝑂̅̅𝑇̅
2. ̅𝑁̅̅𝑂̅ is congruent to ̅𝑂̅̅𝑇̅
•∠𝐸 is congruent to ∠𝑂
•∠𝑁 is congruent to ∠𝑂
•̅𝐸̅̅𝑇̅ is not congruent to 𝑁̅̅𝐸̅

14. Identify which of the following set of points forms
a parallelogram.
1. A(-4,-4) ; B(-4,4) ; C(4,4) ; D(4,-4)
2. E(-5,-2) ; F(-5,2) ; G(5,2) ; H(5,-2)
3. I(-3,-3) ; J(-3,0) ; K(4,2) ; L(4,-3)
4. M(-7,-3) ; N(-4,0) ; O(1,0) ; P(-2,-3)
5. Q(0,0) ; R(0,6) ; S(3,6) ; T(4,0)

15. Study the Parallelogram
105°
105°
75°
75°

16. D
C
B
A
15 cm
10 cm

17. DRAW ME!
Quadrilateral ABCD so that 𝑨𝑩 ≅ 𝑫𝑪 and 𝑨𝑫 ≅ 𝑩𝑪
Steps:
a. Draw ∠DAB.
b. Locate C so that 𝑫𝑪 ≅ 𝑨𝑩𝒂𝒏𝒅 𝑪𝑩 ≅ 𝑫𝑨.
Hint: From D, strike an arc with radius AB. From B,
strike an arc with radius DA.

18. DRAW ME!
W
X Y
Z
Draw quadrilateral EFGH so that:
∠H ≅∠WYZ; ∠G ≅ ∠XYW
∠F ≅ ∠WYZ; ∠E ≅ ∠XYW

19. A quadrilateral is a parallelogram if both pairs of opposite
sides are congruent.
A quadrilateral is a parallelogram if both pairs of opposite
angles are congruent.
A quadrilateral is a parallelogram if both pairs of
consecutive angles are supplementary.
A quadrilateral is a parallelogram if the diagonals bisect
each other.
A quadrilateral is a parallelogram if each diagonals divides
a parallelogram into two congruent triangles.
A quadrilateral is a parallelogram if one pair of opposite
sides are both congruent and parallel.

20. D
C
B
A
Identify angles which are congruent
and supplementary.

21. Mang Juan is a farmer in Caramoran who owns a field in a shape of
parallelogram named as ABCD as shown in the figure. If he is standing at point A
and angle B is given. How will you find m∠𝐴?
Is it possible to find the measure of an unknown angle of a parallelogram applying
its properties?

22. D
C
B
A
Given the parallelogram ABCD, if ∠B = (2a + 25)o and 𝑚∠D = (3a – 15) o ,
1. find the value of a.
2. What is m∠D?
What is m∠B?

23. D
C
B
A
Given the parallelogram ABCD, if ∠A measures 60o, find:
m∠B
m∠ C
m∠D Questions:
What property of parallelogram did you apply to solve for m∠ B, m∠C, and m∠D?

24. R
E
H
O
Given:
Parallelogram HERO
𝑯𝑬 = 𝟐𝟒 𝒄𝒎
𝑬𝑹 = 𝟏𝟓 𝒄𝒎
Find:
𝑯𝑶
𝑹𝑶
Processing questions:
How did you find 𝑯𝑶
and 𝑹𝑶 ?
How is 𝑯𝑬 and 𝑹𝑶 related?
How is 𝑯𝑶 and 𝑬𝑹 related?

25. R
E
H
O
Given:
Parallelogram HERO
𝑯𝑬 = (𝟑𝑿 − 𝟓) 𝒄𝒎
𝑹𝑶 = (𝑿 + 𝟕) 𝒄𝒎
Find:
X
𝑯𝑬
𝑹𝑶
Processing questions:
How did you solve for the value y?
How is 𝑯𝑬 and 𝑹𝑶 related?

26. R
E
H
O
Given:
Parallelogram HERO
𝑯𝑬 = (𝟑𝑿 − 𝟓) 𝒄𝒎
𝑹𝑶 = (𝑿 + 𝟕) 𝒄𝒎
Find:
X
𝑯𝑬
𝑹𝑶
Processing questions:
How did you solve for the value y?
How is 𝑯𝑶 and 𝑬𝑹 related?

27. R
E
H
O
Given:
Parallelogram HERO
𝑯𝑬 = (𝟐𝒚 − 𝟕) 𝒄𝒎
𝑹𝑶 = (𝒚 + 𝟑) 𝒄𝒎
Find:
y
𝑬𝑹
𝑯𝑶
Processing questions:
How did you solve for the value y?
How is 𝑯𝑶 and 𝑬𝑹 related?

28. Mang Dado is a farmer in Caramoran who owns a field in a shape of
parallelogram named as ABCD as shown in the figure. If he is
standing at point A and he wants to go home to rest by travelling in
either way, how many meters will he covers from point A to point C by
travelling any side of the field if 𝐴B= (2x) m, BC= (2y + 25) CD= (3x –
25) m and AD= (3y) m ?

29. R
A
C
E
Given:
Parallelogram CARE.
𝑪𝑨 = 𝟑(𝒙 − 𝟑) 𝒄𝒎
𝑹𝑬 = (𝟐𝒙 + 𝟏𝟏) 𝒄𝒎
𝑬𝑪 = (𝟓𝒚 − 𝟖) 𝒄𝒎
𝑨𝑹 = (𝟑𝒚 + 𝟏𝟒) 𝒄𝒎
Find:
X and y
𝑪𝑨
𝑨𝑹

30. Using properties of parallelogram,
• Diagonals of a parallelogram
bisect each other
• A diagonal of a parallelogram
divides the parallelogram into
two congruent triangles.
Given the parallelogram MATH
with the intersection of diagonals
O,
identify which of the segments
formed by intersecting diagonals
are congruent.
Identify which triangles are
congruent.
O

31. R
E
H
O
Given: parallelogram
HERO
Diagonals HR and EO
meet at
Z. OZ is 8 cm and HR is
13 cm.
How long is EO?
How long is HZ?
Z

32. R
E
H
O
Given: Parallelogram HERO
OZ = (4a – 5) cm
EZ= (3a + 5) cm
Find:
A
OZ
EZ
OE
If HE = 50 cm and ER = 60 cm,
find the perimeter of ∆HOR
Z

33. R
E
H
O
Z
Given:
Parallelogram
HERO
̅𝐻̅̅𝑍̅ = (12b + 1) cm
̅𝑅̅̅𝑍̅ = (2b + 21) cm
Find:
b
•̅𝐻̅̅𝑍̅
•̅𝑅̅̅𝑍̅
•̅𝐻̅̅𝑅̅

34. R
E
H
O
Z
Given: Parallelogram HERO
OZ = (4a – 5) cm
EZ= (3a + 5) cm
Find:
1. a
2. OZ
3. EZ
4. OE
5. If HE = 50 cm and ER = 60 cm, find
the perimeter of ∆HOR
Processing questions:
a. How did you find the value of a?
b. How is OZ and EZ related?
c. How did you find the value of OE?
d. How did you find the perimeter of
∆HOR?

35. Mang Ramon a farmer in Caramoran who owns a field in a
shape of parallelogram named as ABCD with diagonals AC
and BD that intersect at O as shown in the figure. If he
wants to enclose the triangular half by fencing materials
how many meters will he used if AB= 30 m, BC = 45 m, C if
AO= (3x - 6) m and OC= (2x+ 6) m?
O