Maths Assignment Class VIII | Quadrilateral

 Math Assignment  Class VIII  

Understanding Quadrilateral 

Important extra questions on Quadrilateral class 8 strictly according to the DAV board and CBSE Board, necessary for board examinations.

Understanding Quadrilateral 

chapter - 11, class - 8

Question 1

(i) Two adjacent angles of a parallelogram are (5x + 65)^o and (85 – 2x)^o. Find the measure of each angle of a parallelogram.

(ii) Two adjacent angles of a parallelogram are of measure (4x + 2)^o and (3x - 4)^o. Find the measure of each angle of the parallelogram.

(iii) Two adjacent angles of a parallelogram are in the ratio 1 : 2. Find all the angles of parallelogram.

Question 2

A pair of adjacent sides of a rectangle is in the ratio of 5 : 12. If the length of the diagonal is 26 cm. Find the lengths of sides and perimeter of the rectangle.

Question 3

ABCD is a rectangle in which DP and BQ are perpendiculars from D and B respectively on diagonal AC. Show that :

(i) △ADP ≅ △CBQ

(ii) ∠ADP = ∠CBQ

(iii) DP = BQ

Question 4

In the given figure ABCD is a parallelogram. If ∠DAB= 75^o and ∠DBC= 60^o, Calculate ∠CDB and ∠ADB

Question 5

PQRS is a rectangle. ST is perpendicular from S on diagonal PR. If ∠PST : ∠RST = 4 : 5. Find ∠TPQ.

Question 6

Two adjacent angles of a rhombus are in the ratio 2 : 3. Find all the angles of the rhombus. 

Question 7

In the given figure both RIsK and ClUE are parallelogram. Find the value of x.

Question 8

PQRS is a rhombus. If ∠PSQ = 55^o, find all the angles of the rhombus.

Question 9

In the given parallelogram PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR  and diagonal PR.

Question 10

In the figure, l || m and 't' is the transversal. The angle bisectors of interior angles intersect at P and Q. Find the values of angles x and y.

Question 11

Find the measure of ∠x  in the given figure.

Question 12

The lengths of a pair of adjacent sides of a rectangle are in the ratio 3 : 4. If its diagonal is 50 cm, find the lengths of the sides and hence, the perimeter of the rectangle.

Question 13

PQRS is a rhombus. If ∠PSQ = 40^o, find the angles of the rhombus.

Question 14

Exterior angle of a parallelogram is 100^o. Find the angles of parallelogram ?

Question 15

The diagonals of a rectangle ABCD intersect at O. If ∠BOC = 68^o, find ∠ODA.

Question 16

ABCD is a rhombus and its diagonals intersect at O.

(i) Is △BOC  ≌ △DOC ? State the congruence condition used.

(ii) Also state, if ∠BCO = ∠DCO

Question 17

In the given figure the exterior angle ABX of parallelogram ABCD is 70^o and O is the mid point of diagonal BD, Find ∠BAD and ∠ADC. Also find the length of diagonal AB, when OC = 3 cm.

Question 18

In given figure, ABCD is a rectangle and diagonals intersect at O. If ∠AOB = 108^o, find

(i) ∠ABO    (ii) ∠ADO     (iii) ∠OCB

Question 19

In the given figure, PQRS is a rectangle, If ∠PRQ = 30^o , find the value of ∠PQS.

 

Question 20

The lengths of the diagonals of a rhombus are in ratio 6 : 8. If its perimeter is 40 cm. Find the length of the shorter diagonal.

Question 21

Find the measure of x in the given figure 

Question 22.

Diagonals of a rhombus intersect each other at O. If ∠BOC = 68^o , find ∠ODA.

Question 23.

A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.

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