#### Chapters

Chapter 2: Exponents

Chapter 3: Squares and Square Root

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Sets

Chapter 7: Percent and Percentage

Chapter 8: Profit, Loss and Discount

Chapter 9: Interest

Chapter 10: Direct and Inverse Variations

Chapter 11: Algebraic Expressions

Chapter 12: Identities

Chapter 13: Factorisation

Chapter 14: Linear Equations in one Variable

Chapter 15: Linear Inequations

Chapter 16: Understanding Shapes

Chapter 17: Special Types of Quadrilaterals

Chapter 18: Constructions

Chapter 19: Representing 3-D in 2-D

Chapter 20: Area of a Trapezium and a Polygon

Chapter 21: Surface Area, Volume and Capacity

Chapter 22: Data Handling

Chapter 23: Probability

## Chapter 17: Special Types of Quadrilaterals

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

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.

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

In rhombus ABCD;

(i) if ∠A = 74° ; find ∠B and ∠C.

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

In square PQRS :

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

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

ABCD is a rectangle, if ∠BPC = 124°

Calculate : (i) ∠BAP (ii) ∠ADP

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

(i) ∠ACB

(ii) ∠DAC

(iii) ∠ADC.

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

PQRS is a parallelogram whose diagonals intersect at M.

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

(i) ∠RPS

(ii) ∠PRS

(iii) ∠PSR.

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

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

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

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

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

Prove that the diagonals of a parallelogram bisect each other.

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

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

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.

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.

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.

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.

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

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

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

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

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

Selina solutions for Concise Mathematics Class 8 ICSE chapter 17 (Special Types of Quadrilaterals) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Concise Mathematics Class 8 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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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..

Using Selina Class 8 solutions Special Types of Quadrilaterals exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 8 prefer Selina Textbook Solutions to score more in exam.

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