# Selina solutions for Concise Mathematics Class 8 ICSE chapter 17 - Special Types of Quadrilaterals [Latest edition]

#### Chapters ## Chapter 17: Special Types of Quadrilaterals

Exercise 17
Exercise 17 [Pages 198 - 199]

### Selina solutions for Concise Mathematics Class 8 ICSE Chapter 17 Special Types of Quadrilaterals Exercise 17 [Pages 198 - 199]

Exercise 17 | Q 1 | Page 198

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.

Exercise 17 | Q 2 | Page 198

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

Exercise 17 | Q 3 | Page 198

In rhombus ABCD;
(i) if ∠A = 74° ; find ∠B and ∠C.
(ii) if AD = 7.5 cm ; find BC and CD.

Exercise 17 | Q 4 | Page 198

In square PQRS :
(i) if PQ = 3x – 7 and QR = x + 3 ; find PS
(ii) if PR = 5x and QR = 9x – 8. Find QS

Exercise 17 | Q 5 | Page 198

ABCD is a rectangle, if ∠BPC = 124°
Calculate : (i) ∠BAP (ii) ∠ADP Exercise 17 | Q 6 | Page 198

ABCD is a rhombus. If ∠BAC = 38°, find :
(i) ∠ACB
(ii) ∠DAC Exercise 17 | Q 7 | Page 198

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

Exercise 17 | Q 8 | Page 198

PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :

(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.

Exercise 17 | Q 9 | Page 198

Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.

Exercise 17 | Q 10 | Page 198

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

Exercise 17 | Q 11.1 | Page 198

ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?

Exercise 17 | Q 11.2 | Page 198

ABCD is a parallelogram. What kind of quadrilateral is it if: AC is perpendicular to BD but is not equal to it?

Exercise 17 | Q 11.3 | Page 198

ABCD is a parallelogram. What kind of quadrilateral is it if: AC = BD but AC is not perpendicular to BD?

Exercise 17 | Q 12 | Page 199

Prove that the diagonals of a parallelogram bisect each other.

Exercise 17 | Q 13 | Page 199

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

Exercise 17 | Q 14 | Page 199

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

Exercise 17 | Q 15 | Page 199

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

(ii) DE bisects and ∠ADC and
(iii) Angle DEC is a right angle.

Exercise 17 | Q 16 | Page 199

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°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.

Exercise 17 | Q 17 | Page 199

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.

Exercise 17 | Q 18 | Page 199

The given figure shows 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.

Exercise 17 | Q 19 | Page 199

The given figure shows a rhombus ABCD in which angle BCD = 80°. Find angles x and y. Exercise 17 | Q 20 | Page 199

Use the information given in the alongside diagram to find the value of x, y, and z. Exercise 17 | Q 21 | Page 199

The following figure is a rectangle in which x: y = 3: 7; find the values of x and y. Exercise 17 | Q 22 | Page 199

In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that: (i) ∠EAC = ∠ACB
(ii) ABCE is a parallelogram.

## Chapter 17: Special Types of Quadrilaterals

Exercise 17 ## Selina solutions for Concise Mathematics Class 8 ICSE chapter 17 - Special Types of Quadrilaterals

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Concepts covered in Concise Mathematics Class 8 ICSE chapter 17 Special Types of Quadrilaterals are Properties of Trapezium, Properties of Rectangle, Properties of a Parallelogram, Properties of Rhombus, Property: The diagonals of a square are perpendicular bisectors of each other..

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