Properties Of Parallelograms Worksheet Answers

PROPERTIES OF PARALLELOGRAMS WORKSHEET

Trouble 1 :

In the parallelogram given below,  discover ∠B, ∠C and ∠D.

Problem 2 :

In the parallelogram ABCD given below, find ∠A, ∠B, ∠C and ∠D.

Trouble iii :

In the parallelogram given below, detect the measures of ∠ABO and ∠ACB.

Problem 4 :

The perimeter of the parallelogram ABCD shown below is 30 units and the length of the side AB is 9 units, find the length of other sides of the parallelogram.

Problem 5 :

In the parallelogram given below, discover the value of x, measures of∠A and ∠C.

Problem 6 :

In the parallelogram given below,

AO = x + forty

OC = 2x + xviii

Find the length of AO and OC.

Problem 7 :

In two adjacent angles of a parallelogram, if 1 bending is four times of the other, then notice the measures of the 2 angles.

Problem 8 :

In the parallelogram given to a higher place, discover the lengths of the sides GJ and How-do-you-do (in cm).

Problem 9 :

In the parallelogram given beneath, find the values of x and y.

Problem 10 :

In the parallelogram given below, find the values of x and y.

1. Respond :

In a parallelogram, side by side angles are supplementary.

In the higher up parallelogram, ∠A and ∠B are adjacent angles.

∠A + ∠B = 180°

65° + ∠B = 180°

∠B = 115°

Because opposite angles are coinciding, nosotros accept

∠C = ∠A ∠C = 65 °

∠D = ∠B ∠D = 115 °

Hence, the measures of ∠B, ∠C and ∠D are 115°, 6 v° and 115° respectively.

ii. Answer :

In a parallelogram, adjacent angles are supplementary.

In the above parallelogram, ∠A and ∠B are adjacent angles.

x + 2x = 180°

3x = 180°

 x = 60 °

The measure of angle ∠A is

= 10

= lx °

The measure of bending ∠B is

= 2x

= 2 ⋅ lx °

= 120 °

Co-ordinate to the backdrop of parallelogram, the contrary angles are coinciding.

∠C = ∠A ∠C = threescore °

∠D = ∠B ∠D = 120 °

Hence, the measures of ∠A, ∠B, ∠C  and ∠D are 60 °, 120 °, 60 ° and 120 ° respectively.

three. Answer :

In the parallelogram given above ∠AOB and ∠COD are vertically opposite angles.

Because vertically opposite angles are equal, we have

∠AOB = ∠COD

∠AOB = 105 °

In triangle ABO, we have

∠OAB + ∠AOB + ∠ABO = 180 °

Substitute ∠OAB = xxx ° and ∠AOB = 105 °.

thirty °  + 105 °  + ∠ABO = 180°

135 ° + ∠ABO = 180 °

∠ABO = 45 °

In the parallelogram given above, Advert||BC, AC is transversal and ∠OCB and ∠OAD are alternating interior angles.

If two parallel lines are cut by a transversal, alternate interior angles are equal.

∠OCB = ∠OAD

In the parallelogram given to a higher place, ∠OAD = 45 °.

Then,

∠OCB = 45 °

Because ∠OCB  ≅ ∠ACB, we have

∠ACB = 45°

Hence, the measures of ∠ABO and ∠ACB are 45 ° each.

4. Answer :

Given : Perimeter of the parallelogram is xxx units.

AB + BC + CD + AD = 30 ----(1)

Because it is parallelogram, length of contrary sides must be equal.

AB = CD

AD = BC

Given : AB = 9 units.

In a parallelogram, opposite sides are equal, so AB = CD.

AB = CD = half dozen.

(1)----> nine + BC + 9 + AD = xxx

18 + BC + AD = 30

BC + AD = 12

Because AD = BC,

AD + AD = 12

2 ⋅ Ad = 12

AD = 6

Then, the length of BC is also vi units.

Hence, the length of CD is 9 units, Advertizing and BC are 6 units each.

v. Reply :

According to the backdrop of parallelogram, reverse angles are equal.

∠B = ∠D

(10 + 29)° = 75 °

10 + 29 = 75

x = 46

In a parallelogram, a djacent angles are supplementary.

∠D + ∠C = 180°

75° + ∠C = 180 °

∠C = 105°

In a parallelogram, contrary  angles are equal.

∠A = ∠C

∠A = 105 °

Hence, the measures of∠A and ∠C are 105 ° each .

6. Answer :

AO = x + 40

OC = 2x + 18

According to the properties of parallelogram, the diagonals bisect each other.

AO = OC

ten + 40 = 2x + 18

40 = ten + 18

10 = 22

Length of AO :

AO = x + 40

AO = 22 + 40

AO = 62

Length of OC :

OC = 2x + eighteen

OC = ii ⋅ 22 + 18

OC = 44 + 18

OC = 62

Hence, the lengths of AO and OC are 62 units each.

vii. Answer :

Let x be one of the angles.

Then, the adjacent angle of ten is 4x

In a parallelogram, a djacent angles are supplementary.

x + 4x = 180 °

5x = 180 °

x = 36 °

Then, the measure out of the adjacent angle is

= 4 x

= iv ⋅ 36 °

= 144 °

Hence, the measures of the two adjacent angles are 36 ° and 144 °.

8. Reply :

According to the properties of parallelogram, the length of reverse sides are equal.

Length of AB = Length of CD

5x = x + 44

4x = 44

x = 11

Length of AB:

AB = 5x

= 5 ⋅ 11

= 55

Because opposite sides are equal, the length of CD is also 55 units.

Hence, the lengths of AB and CD are 55 units each.

9.Answer :

According to the properties of parallelogram, the diagonals of a parallelogram bifurcate each other.

From the diagonal Air conditioning, nosotros accept

ten + y = 2y - 2

x =  y - two ----(i)

From the diagonal BD, we have

3x = 2y ----(2)

Substitute x = y - 2 in (two).

iii(y - 2) = 2y

3y - 6 = 2y

y = 6

Substitute y = half dozen in (1).

x = vi - 2

x = four

Hence, the value of x is iv and y is 6.

10. Respond :

In the parallelogram given to a higher place, the measure of angle Y is

∠Y = 45 ° + 70 °

∠Y = 115°

In a parallelogram, a djacent angles are supplementary.

Because ∠F and ∠Y are supplementary, we accept

∠F + ∠Y = 180 °

Substitute ∠F = ( 7x - 5) ° and∠Y = 115°.

(7x - 5)° + 115° = 180°

7x - 5 + 115 = 180

7x + 110 = 180

7x = seventy

x = 10

The measure out of angle ∠F :

= (7x - five) °

= (7 ⋅ x - 5) °

= (70 - five) °

= 65 °

In a parallelogram, opposite angles are equal.

∠D = ∠F

(5y) ° =65°

5y = 65

y = xiii

Hence, the value of x is ten and y is 13.

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Properties Of Parallelograms Worksheet Answers,

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