3. 3. Use properties to find measures of angles,
sides and other quantities involving parallelograms
PROPERTIES OF PARALLELOGRAMS
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
OBJECTIVES:
At the end of the session, teachers should be
able to:
1. Define quadrilateral and parallelogram
2. Identify properties of parallelograms
4. 1. What are quadrilaterals? What are parallelograms?
PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
3. How can we use these properties to find the
measures of angles, sides and other quantities
involving parallelograms?
2. What are the properties of parallelograms?
5. 4. Write TRUE if the statement is true and write FALSE if the
statement is false.
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
PROPERTIES OF PARALLELOGRAM
STATEMENT TRUE OR FALSE
1. A quadrilateral is a parallelogram if both pairs of opposite
sides are parallel.
2. A quadrilateral is a parallelogram if both pairs of opposite
sides are congruent.
3. A quadrilateral is a parallelogram if both pairs of opposite
angles are congruent.
4. A quadrilateral is a parallelogram if any two consecutive
angles are complementary.
5. A quadrilateral is a parallelogram if exactly one pair of
adjacent sides is perpendicular.
6. What is QUADRILATERAL?
- a closed plane figure consisting
of four line segments or sides
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
PROPERTIES OF PARALLELOGRAM
7. DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
PROPERTIES OF PARALLELOGRAM
parallelogram
rectangle
rhombus
square
trapezoid
kite
8. What is PARALLELOGRAM?
PROPERTIES OF PARALLELOGRAM
- a quadrilateral with two
pairs of opposite sides
that are parallel
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
9. DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
PROPERTIES OF PARALLELOGRAM
PARALLELOGRAM
ABCD
“parallelogram ABCD”
A
D
C
B
AD//BC & AB//DC
It has 4 vertices.
It has 4 angles.
It has 4 sides.
10. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
What are the poperties of Parallelogram?
In a parallelogram,
any two opposite
sides are congruent.
Parallelogram Property 1
A D
C
B
11. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
In a parallelogram, any two
opposite sides are congruent.
D
C
A
B
AB ≅ DC
AD ≅ BC
Parallelogram Property 1
12. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
In a parallelogram,
any two opposite
angles are congruent.
Parallelogram Property 2
D
C
A
B
13. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
In a parallelogram, any two
opposite angles are congruent.
D
C
A
B
∠A ≅∠𝐶
∠B ≅∠𝐷
Parallelogram Property 2
14. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
In a parallelogram,
any two consecutive
angles are
supplementary.
Parallelogram Property 3
D
C
A
B
15. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
Parallelogram Property 3
In a parallelogram, any two
consecutive angles are supplementary.
D
C
A
B
m∠A + m∠𝐵 = 180°
m∠A + m∠𝐷 = 180°
m∠D + m∠𝐶 = 180°
m∠C + m∠𝐵 = 180°
16. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
Parallelogram Property 4
The diagonals of
parallelogram bisect
each other.
D
C
A
B
17. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
Parallelogram Property 4
The diagonals of parallelogram
bisect each other.
D
C
A
B
E
AE = EC
BE = ED
18. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
A diagonal of a
parallelogram divides the
parallelogram into two
congruent triangles.
Parallelogram Property 5
D
C
A
B
19. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
A diagonal of a
parallelogram divides the
parallelogram into two
congruent triangles.
Parallelogram Property 5
D
C
A
B
∆ABD ≅ ∆DCB
20. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
5. A diagonal of a parallelogram divides the parallelogram
into two congruent triangles.
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 parallelogram bisect each other.
Properties of Parallelogram
21. Write TRUE if the statement is true and write FALSE if the
statement is false.
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
PROPERTIES OF PARALLELOGRAM
STATEMENT TRUE OR FALSE
1. A quadrilateral is a parallelogram if both pairs of opposite
sides are parallel.
2. A quadrilateral is a parallelogram if both pairs of opposite
sides are congruent.
3. A quadrilateral is a parallelogram if both pairs of opposite
angles are congruent.
4. A quadrilateral is a parallelogram if any two consecutive
angles are complementary.
5. A quadrilateral is a parallelogram if exactly one pair of
adjacent sides is perpendicular.
TRUE
TRUE
TRUE
FALSE
FALSE
22. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
Let’s apply properties of parallelograms to find some
measures. Complete the satement about ABCD.
D
C
A
B
E
1. If AB= 19,then CD=_____.
2. If AE= 13,then EC=_____.
3. If DE= 7.5,then BD=_____.
4. If BC= x,then AD=_____.
5. If CE= y,then AC=_____.
6. If BD= k,then BE=_____.
23. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
Let’s apply properties of parallelograms to find some
measures. Complete the satement about ABCD.
D
C
A
B
E
1. If AB= 19,then CD = 19.
2. If AE= 13,then EC = 13.
3. If DE= 7.5,then BD = 15.
4. If BC= x,then AD = x .
5. If CE= y,then AC = 2y.
6. If BD= k,then BE = k/2.
24. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
Given ABCD with ∠D=50°. AC & BD are angle bisectors.
Find the measure of each of the following angles:
1. ∠𝐵
2. ∠𝐷𝐴𝐵
4. ∠𝐷𝐶𝐵
5. ∠𝐴𝐶𝐷
6.∠𝐴𝐶𝐵
3. ∠𝐷𝐴𝐶
25. PROPERTIES OF PARALLELOGRAM
DEPARTMENT OF EDUCATION-SCHOOLS DIVISION OF SOUTH COTABATO
Given ABCD with ∠D=50°. AC is the angle bisector
∠A &∠C and BD is the angle bisectors of ∠B &∠D .
Find the measure of each of the following angles:
1. ∠𝐵 = 𝟓𝟎°
2. ∠𝐷𝐴𝐵 = 𝟏𝟑𝟎°
4. ∠𝐷𝐶𝐵 = 𝟏𝟑𝟎°
5. ∠𝐴𝐶𝐷 = 𝟔𝟓°
6. ∠𝐴𝐶𝐵 = 65°
3. ∠𝐷𝐴𝐶 = 𝟔𝟓°
