# Understanding Quadrilaterals NCERT Questions

NCERT TEXT BOOK EXERCISES

EXERCISE-3.1

1. Given here are some figures.

Classify each of them on the basis of the following.

(a) Simple curve

(b) Simple closed curve

(c) Polygon

(d) Convex polygon

(e) Concave polygon

1. How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle

1. What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
2. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
 Figure Side Angle sum Figure Side Angle sum 3 180° 5 3 × 180° = (5 − 2) × 180° 4 2 × 180° = (4 − 2) × 180° 6 4 × 180° = (6 − 2) × 180°

What can you say about the angle sum of a convex polygon with number of sides?

(a) 7                    (b) 8                             (c) 10                           (d) n

1. What is a regular polygon?

State the name of a regular polygon of

(i) 3 sides            (ii) 4 sides         (iii) 6 sides

1. Find the angle measure xin the following figures.

P7.

(a)                                            (b)

(a) find x + z

(b) find x + z + w

EXERCISE-3.2

1. Find xin the following figures.
 (a) (b)

1. Find the measure of each exterior angle of a regular polygon of

(i) 9 sides            (ii) 15 sides

1. How many sides does a regular polygon have if the measure of an exterior angle is 24°?
2. How many sides does a regular polygon have if each of its interior angles is 165°?
3. (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?

(b) Can it be an interior angle of a regular polygon? Why?

1. (a) What is the minimum interior angle possible for a regular polygon?

(b) What is the maximum exterior angel possible for a regular polygon?

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 = …

1. Consider the following parallelograms. Find the values of the unknowns x, y, z.
2. 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°?

1. Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
2. 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.
3. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
4. The adjacent figure HOPE is a parallelogram. Find the angle measures xyand z. State the properties you use to find them.
5. The following figures GUNS and RUNS are parallelograms. Find and y. (Lengths are in cm)

9.

In the above figure both RISK and CLUE are parallelograms. Find the value of x.

1. Explain how this figure is a trapezium. Which of its two sides are parallel?
2. Find m∠C in the following figure if
3. Find the measure of ∠P and ∠S, if in the following figure. (If you find m∠R, is there more than one method to find m∠P?)

EXERCISE-3.4

1. State whether True or False.

(a) All rectangles are squares.

(b) All rhombuses are parallelograms.

(c) All squares are rhombuses and also rectangles.

(d) All squares are not parallelograms.

(e) All kites are rhombuses.

(f) All rhombuses are kites.

(g) All parallelograms are trapeziums.

(h) All squares are trapeziums.

1. Identify all the quadrilaterals that have

(a) four sides of equal length

(b) four right angles

1. Explain how a square is.

(ii) a parallelogram

(iii) a rhombus

(iv) a rectangle

1. Name the quadrilaterals whose diagonals.

(i) bisect each other

(ii) are perpendicular bisectors of each other

(iii) are equal

1. Explain why a rectangle is a convex quadrilateral.
2. ABC is a right-angled triangle and O is the midpoint of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).