Ncert solutions mathematics class 8 Solutions for Chapter 3 understanding quadrilaterals

What is the sum of the measures of the angles of a convex quadrilateral?

Q2) How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle

Q3) What is the sum of the measures of the angles of a convex quadrilateral? Will this property

hold if the quadrilateral is not convex? (Make anon-convex quadrilateral and try!)

Q4) Examine the table. (Each figure is divided into triangles and the sum of the angles

deduced from that.)

Part-2

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

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

Q5) What is a regular polygon?

State the name of a regular polygon of

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

Q7)

(i)

Find x+y+z

(ii)

Find x+y+z+w

Q6) Find the angle measure x in the following figures.

(i)

(ii)

(iii)

(iv)

Find the angle measure x in the following figure.

Find the angle measure x in the following figure.

Find w + x + y + z.

How many diagonals does a regular hexagon have?

State the name of a regular polygon of 3 sides.

State the name of a regular polygon of 6 sides.

Q1) Given here are some figures.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

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

How many diagonals does a convex quadrilateral have?

Find each of them on the basis of the simple closed curve.

Find each of them on the basis of the convex polygon .

Find each of them on the basis of the simple curve.

How many diagonals does a triangle have?

Find each of them on the basis of the polygon .

Find each of them on the basis of the concave polygon .

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides as 7?

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides as 8?

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides as 10?

State the name of a regular polygon of 4 sides.

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

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

Find x + y + z.

Find the angle measure x in the following figure.

Find the angle measure x in the following figure.

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

How many diagonals does each of the following have?

(a) A convex quadrilateral (b) A regular hexagon (c) A triangle

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

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

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

What is a regular polygon?

State the name of a regular polygon of

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

Find the angle measure x in the following figures.

Q1) Find x in the following figures.

(i)

(ii)

Q4) How many sides does a regular polygon have if each of its interior angles

is 165°?

Q2)Find the measure of each exterior angle of a regular polygon of

(i) 9 sides (ii) 15 sides

Q6)

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

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

Q3) How many sides does a regular polygon have if the measure of an exterior angle is 24°?

Q5)

(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?

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

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

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

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

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

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

Find x.

Find x.

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

Find x in the following figures.

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

(i) 9 sides (ii) 15 sides

How many sides does a regular polygon have if the measure of an exterior angle is 24^{\circ} ?

How many sides does a regular polygon have if each of its interior angles is 165^{\circ} ?

a) Is it possible to have a regular polygon with a measure of each exterior angle as 22^{\circ}?

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

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

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

Consider the following parallelogram. Find the values of the unknown x, y, z

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

AD = ……

Consider the following parallelogram. Find the values of the unknown x, y, z

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

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

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 ∠D + ∠B = 180°?

Check if the given figure is 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 ∠D.

The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of ∠B.

The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of ∠A.

The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of ∠C.

In the following figure, RUNS is a parallelogram. Find x and y. (Lengths are in cm)

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

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

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

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

Consider the following parallelogram. Find the values of the unknown x, y, z

Find the measure of ∠P and ∠S if SP || RQ ?

The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z.

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

Which of its two sides are parallel in the given figure?

Find ∠C in given figure, if AB || DC ?

Q1)

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 = ……

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

m ∠DAB + m ∠CDA = ……

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

OC = ……

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

∠DCB = ……

Consider the following parallelogram. Find the values of the unknown x, y, z

Consider the following parallelogram. Find the values of the unknown x, y, z

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 = ……

Q2) Consider the following parallelograms. Find the values of the unknowns x, y, z

(i)

(ii)

(iii)

(iv)

(v)

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

Q3) Can a quadrilateral ABCD be a parallelogram, if:

(i) \angle D+\angle B=180\degree?

(ii) AB=DC= 8cm, AD = 4cm and BC = 4.4 cm?

(iii) \angle A=70\degree and\ \angle C=65\degree?

Can a quadrilateral ABCD be a parallelogram if

(i) ∠D + ∠B = 180^{\circ}?

(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

(iii) \angle \mathrm{A}=70^{\circ} \text { and } \angle \mathrm{C}=65^{\circ} ?

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

Q4) Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.

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.

Q5) The measure of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

Q6) Two adjacent angles of a parallelogram have equal measure. Find the measure 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.

Q7) The adjacent figure HOPW is a parallelogram. Find the angle measures x,y and z. State the properties you use to find them.

\angle HOP+70\degree=180\degree

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

Q8) The following figures GUNS and RUNS are parallelograms. Find x and y (Lengths are in cm)

(i)

(ii)

The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

Q9) In the figure, both RISK and CLUE are parallelograms. Find the value of x.

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

Q10) Explain how this figure is a trapezium. Which is its two sides are parallel?

Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)

Find m∠C in Fig 3.33 if AB || DC ?

Q11) FInd m\angle C in figure, if \because\overline{AB}\parallel\overline{DC}

Q12) Find the measure of \angle P\ and\ \angle S\ if\ \overline{SP}\parallel\overline{RQ} in given figure.

(If you find m\angle R is there more than one method to find m\angle P)

Find the measure of ∠P and ∠S if SP || RQ ? in Fig 3.34. (If you find m∠R, is there more than one method to find m∠P?)

State whether True or False:

All rhombuses are kites.

State whether True or False:

All parallelograms are trapeziums.

State whether True or False:

All rectangles are squares.

State whether True or False:

All rhombuses are parallelograms.

State whether True or False:

All squares are not parallelograms.

State whether True or False:

All kites are rhombuses.

State whether True or False:

All squares are rhombuses and also rectangles.

Q1) 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.

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.

Identify all the quadrilaterals that have.

(a) four sides of equal length (b) four right angles

Q2)Identify all the quadrilaterals that have:

(a) four sides of equal lengths.

(b) four right angles.

Q3) Explain how a square is:

(a) a quadrilateral

(b) a parallelogram

(c) a rhombus

(d) a rectangle

Explain how a square is.

(i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle

Q4) Name the quadrilateral whose diagonals:

(i) bisect each other.

(ii) are perpendicular bisectors of each other.

(iii) are equal.

Name the quadrilaterals whose diagonals.

(i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal

Q5) Explain why a rectangle is a convex quadrilateral.

Explain why a rectangle is a convex quadrilateral.

Q6) 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)

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).