NCERT solutions for Mathematics [English] Class 8 chapter 3 - Understanding Quadrilaterals [Latest edition]

Given here are some figures:

Classify each of them on the basis of the following:

1. Simple curve
2. Simple closed curve
3. Polygon
4. Convex polygon
5. Concave polygon

What is a regular polygon?

State the name of a regular polygon of 3 sides.

State the name of a regular polygon of 4 sides.

State the name of a regular polygon of 6 sides.

Find x in the following figure:

Find x in the following figures.

Find the measure of each exterior angle of a regular polygon of 9 sides.

Find the measure of each exterior angle of a regular polygon of 15 sides

How many sides does a regular polygon have if the measure of an exterior angle is 24°?

How many sides does a regular polygon have if each of its interior angles is 165°?

Is it possible to have a regular polygon with measure of each exterior angle as 22°?

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

What is the minimum interior angle possible for a regular polygon? Why?

What is the maximum exterior angle possible for a regular polygon?

Given a parallelogram ABCD. Complete each statement along with the definition or property used.

1. AD = ______
2. ∠DCB = ______
3. OC = ______
4. m∠DAB + m∠CDA = ______

Consider the given parallelogram. Find the values of the unknowns x, y, z.

Consider the given parallelogram. Find the values of the unknowns x, y, z.

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?

Can a quadrilateral ABCD be a parallelogram if AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?

Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

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.

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

The following figure GUNS is a parallelogram. Find x and y. (Lengths are in cm)

The following figure RUNS is parallelogram. Find x and y. (Lengths are in cm) 

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

Explain how this figure is a trapezium. Which of its two sides are parallel?

Find m∠C in the following figure if `bar(AB) || bar(DC)`

Find the measure of ∠P and ∠S, if `bar(SP) || bar(RQ)` in the following figure. (If you find m∠R, is there more than one method to find m∠P?).

All rectangles are squares

All rhombuses are parallelograms.

All squares are rhombuses and also rectangles.

All squares are not parallelograms.

All kites are rhombuses.

All rhombuses are kites.

All parallelograms are trapeziums.

All squares are trapeziums.

Identify all the quadrilateral that have Four sides of equal length

Identify all the quadrilaterals that have four right angles

Explain how a square is a quadrilateral

Explain how a square is a parallelogram

Explain how a square is a rhombus.

Explain how a square is a rectangle

Name the quadrilaterals whose diagonals  bisect each other

Name the quadrilaterals whose diagonals are perpendicular bisectors of each other

Name the quadrilaterals whose diagonals are equal

Explain why a rectangle is a convex quadrilateral.

ABC is a right-angled triangle and O is the mid point 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)