Selina Class 8 ICSE Solutions Mathematics : Chapter 17- Special Types of Quadrilaterals

Class 8: Maths Chapter 17 solutions. Complete Class 8 Maths Chapter 17 Notes.

Selina Class 8 ICSE Solutions Mathematics : Chapter 17- Special Types of Quadrilaterals

Selina 8th Maths Chapter 17, Class 8 Maths Chapter 17 solutions

Exercise 17

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:

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Selina Class 8 ICSE Solutions Mathematics : Chapter 17- Special Types of Quadrilaterals

Download PDF: Selina Class 8 ICSE Solutions Mathematics : Chapter 17- Special Types of Quadrilaterals PDF

Chapterwise Selina Publishers ICSE Solutions for Class 8 Mathematics :

• Chapter 1- Rational Numbers
• Chapter 2- Exponents (Powers)
• Chapter 3- Squares and Square Roots
• Chapter 4- Cubes and Cube-Roots
• Chapter 5- Playing with Number
• Chapter 6- Sets
• Chapter 7- Percent and Percentage
• Chapter 8- Profit, Loss and Discount
• Chapter 9- Simple and Compound Interest
• Chapter 10- Direct and Inverse Variations
• Chapter 11- Algebraic Expressions
• Chapter 12- Algebraic 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 Trapezium and a Polygon
• Chapter 21- Surface Area, Volume and Capacity
• Chapter 22- Data Handling
• Chapter 23- Probability

About Selina Publishers ICSE

Selina Publishers has been serving the students since 1976 and is one of the quality ICSE school textbooks publication houses. Mathematics and Science books for classes 6-10 form the core of our business, apart from certain English and Hindi literature as well as a few primary books. All these books are based upon the syllabus published by the Council for the I.C.S.E. Examinations, New Delhi. The textbooks are composed by a panel of subject experts and vetted by teachers practising in ICSE schools all over the country. Continuous efforts are made in complying with the standards and ensuring lucidity and clarity in content, which makes them stand tall in the industry.