## Selina Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals

**Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 17 Special Types of Quadrilaterals**

### Special Types of Quadrilaterals Exercise 17 – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.

In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x – 7 and CD = 3x +1 ; find the length of CD.

Solution:

Question 2.

In parallelogram PQRS, ∠Q = (4x – 5)° and ∠S = (3x + 10)°. Calculate : ∠Q and ∠R.

Solution:

Question 3.

In rhombus ABCD ;

(i) if ∠A = 74° ; find ∠B and ∠C.

(ii) if AD = 7.5 cm ; find BC and CD.

Solution:

Question 4.

In square PQRS :

(i) if PQ = 3x – 7 and QR = x + 3 ; find PS

(ii) if PR = 5x and QR = 9x – 8. Find QS

Solution:

Question 5.

ABCD is a rectangle, if ∠BPC = 124°

Calculate : (i) ∠BAP (ii) ∠ADP

Solution:

Question 6.

ABCD is a rhombus. If ∠BAC = 38°, find :

(i) ∠ACB

(ii) ∠DAC

(iii) ∠ADC.

Solution:

Question 7.

ABCD is a rhombus. If ∠BCA = 35°. find ∠ADC.

Solution:

Question 8.

PQRS is a parallelogram whose diagonals intersect at M.

If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :

(i) ∠RPS

(ii) ∠PRS

(iii) ∠PSR.

Solution:

Question 9.

Given : Parallelogram ABCD in which diagonals AC and BD intersect at M.

Prove : M is mid-point of LN.

Solution:

Question 10.

In an Isosceles-trapezium, show that the opposite angles are supplementary.

Solution:

Question 11.

ABCD is a parallelogram. What kind of quadrilateral is it if :

(i) AC = BD and AC is perpendicular to BD?

(ii) AC is perpendicular to BD but is not equal to it?

(iii) AC = BD but AC is not perpendicular to BD?

Solution:

Question 12.

Prove that the diagonals of a parallelogram bisect each other.

Solution:

Question 13.

If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.

Solution:

Question 14.

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

Solution:

Question 15.

In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that :

(i) AE = AD,

(ii) DE bisects and ∠ADC and

(iii) Angle DEC is a right angle.

Solution:

Question 16.

In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.

Show that:

(i) ∠PSB + ∠SPB = 90°

(ii) ∠PBS = 90°

(iii) ∠ABC = 90°

(iv) ∠ADC = 90°

(v) ∠A = 90°

(vi) ABCD is a rectangle

Thus, the bisectors of the angles of a parallelogram enclose a rectangle.

Solution:

Question 17.

In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:

(i) AX = YC

(ii) AX is parallel to YC

(iii) AXCY is a parallelogram.

Solution:

Question 18.

The given figure shows a parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN.

Prove that:

(i) ∆DMC = ∆BNA and so CM = AN

(ii) ∆AMD = ∆CNB and so AM CN

(iii) ANCM is a parallelogram.

Solution:

Question 19.

The given figure shows a rhombus ABCD in which angle BCD = 80°. Find angles x and y.

Solution:

Question 20.

Use the information given in the alongside diagram to find the value of x, y and z.

Solution:

Question 21.

The following figure is a rectangle in which x : y = 3 : 7; find the values of x and y.

Solution:

Question 22.

In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that:

(i) ∠EAC = ∠ACB

(ii) ABCE is a parallelogram.

Solution: