Detailed Solutions for Class 8th NCERT Mathematics – Chapter 3 – Understanding Quadrilaterals – Exercise 3.3
1. Given a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD = …… (ii) ∠ DCB = …… (iii) OC = …… (iv) m ∠DAB + m ∠CDA = ……
Solution:
(i) AD = BC, because opposite sides of a parallelogram are equal.
(ii) ∠ DCB = BAD, because opposite angles of a parallelogram are equal.
(iii) OC = OA, because diagonals of a parallelogram bisect each other.
(iv) m ∠DAB + m ∠CDA = 180, because adjacent angles of parallelogram are supplementary.
2. Consider the following parallelograms. Find the values of the unknowns x, y, z.
3. Can a quadrilateral ABCD be a parallelogram if
(i) ∠D + ∠B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
(iii) ∠A = 70° and ∠C = 65°?
4. Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
9.
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
10. Explain how this figure is a trapezium. Which of its two sides are parallel?
11. Find m∠C in Figure if AB is parallel to DC .
12. Find the measure of ∠P and ∠S if SP is parallel to RQ in Figure
(If you find m∠R, is there more than one method to find m∠P?)
You can find the solution for class 7th Mathematics from here
You can find the solutions for previous exercise from here
- Rational Numbers – Chapter 1 – Exercise 1.1
- Chapter 1 – Rational Numbers – Exercise 1.2
- Linear Equations in one variable – Chapter 2 – Exercise 2.1
- Chapter 2 – Linear Equations in one variable – Exercise 2.2
- Linear Equations in one variable – Chapter 2 – Exercise 2.3
- Chapter 2 – Linear Equations in one variable – Exercise 2.4
- Linear Equations in one variable – Chapter 2 – Exercise 2.5
- Chapter 2 – Linear Equations in one variable – Exercise 2.6
- Understanding Quadrilaterals – Chapter 3 – Exercise 3.1
- Chapter 3 – Understanding Quadrilaterals – Exercise 3.2
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