# RD Sharma solutions for Class 8 Maths chapter 17 - Understanding Shapes-III (Special Types of Quadrilaterals) [Latest edition]

#### Chapters ## Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Exercise 17.1Exercise 17.2Exercise 17.3
Exercise 17.1 [Pages 9 - 12]

### RD Sharma solutions for Class 8 Maths Chapter 17 Understanding Shapes-III (Special Types of Quadrilaterals) Exercise 17.1 [Pages 9 - 12]

Exercise 17.1 | Q 1 | Page 9

Given below is a parallelogram ABCD. Complete each statement along with the definition or property used.
(ii) ∠DCB =
(iii) OC =
(iv) ∠DAB + ∠CDA = Exercise 17.1 | Q 2.1 | Page 9

The following figure is parallelogram. Find the degree values of the unknowns xyz. Exercise 17.1 | Q 2.2 | Page 9

The following figure is parallelogram. Find the degree values of the unknown xyz Exercise 17.1 | Q 2.3 | Page 9

The following figure is parallelogram. Find the degree values of the unknown xyz Exercise 17.1 | Q 2.4 | Page 9

The following figure is parallelogram. Find the degree values of the unknown xyz Exercise 17.1 | Q 2.5 | Page 9

The following figure is parallelogram. Find the degree values of the unknown xyz Exercise 17.1 | Q 2.6 | Page 9

The following figure is parallelogram. Find the degree value of the unknown xyz Exercise 17.1 | Q 3.1 | Page 10 Exercise 17.1 | Q 3.2 | Page 10 Exercise 17.1 | Q 3.3 | Page 10 Exercise 17.1 | Q 4 | Page 10

In the adjacent figure HOPE is a parallelogram. Find the angle measures x,y and z. State the geometrical truths you use to find them. Exercise 17.1 | Q 5.1 | Page 10

In the following figure GUNS and RUNS are  parallelogram. Find x and y Exercise 17.1 | Q 5.2 | Page 10

In the following figure GUNS and RUNS are  parallelogram. Find x and y Exercise 17.1 | Q 6 | Page 10

In the following figure RISK and CLUE are parallelograms. Find the measure of x. Exercise 17.1 | Q 7 | Page 10

Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of each angle of the parallelogram.

Exercise 17.1 | Q 8 | Page 10

If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.

Exercise 17.1 | Q 9 | Page 10

The measure of one angle of a parallelogram is 70°. What are the measures of the remaining angles?

Exercise 17.1 | Q 10 | Page 10

Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.

Exercise 17.1 | Q 11 | Page 10

In a parallelogram ABCD, ∠D = 135°, determine the measure of ∠A and ∠B.

Exercise 17.1 | Q 12 | Page 11

ABCD is a parallelogram in which ∠A = 70°. Compute ∠BC and D.

Exercise 17.1 | Q 13 | Page 11

The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.

Exercise 17.1 | Q 14 | Page 11

All the angles of a quadrilateral are equal to each other. Find the measure of each. Is the quadrilateral a parallelogram? What special type of parallelogram is it?

Exercise 17.1 | Q 15 | Page 11

Two adjacent sides of a parallelogram are 4 cm and 3 cm respectively. Find its perimeter.

Exercise 17.1 | Q 16 | Page 11

The perimeter of a parallelogram is 150 cm. One of its sides is greater than the other by 25 cm. Find the length of the sides of the parallelogram.

Exercise 17.1 | Q 17 | Page 11

The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.

Exercise 17.1 | Q 18 | Page 11

Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)°. Find the angles of the parallelogram.

Exercise 17.1 | Q 19 | Page 11

In a parallelogram ABCD, the diagonals bisect each other at O. If ∠ABC = 30°, ∠BDC = 10° and ∠CAB = 70°. Find:
DAB, ∠ADC, ∠BCD, ∠AOD, ∠DOC, ∠BOC, ∠AOB, ∠ACD, ∠CAB, ∠ADB, ∠ACB, ∠DBC and ∠DBA.

Exercise 17.1 | Q 20 | Page 11

Find the angles marked with a question mark shown in Fig. 17.27 Exercise 17.1 | Q 21 | Page 11

The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram. Exercise 17.1 | Q 22 | Page 11

In the following figure, ABCD and AEFG are parallelograms. If ∠C = 55°, what is the measure of ∠F? Exercise 17.1 | Q 23 | Page 11

In the following figure, BDEF and DCEF are each a parallelogram. Is it true that BD = DC? Why or why not? Exercise 17.1 | Q 24 | Page 12

In Fig. 17.29, suppose it is known that DE = DF. Then, is ΔABC isosceles? Why or why not?

Exercise 17.1 | Q 25 | Page 12

Diagonals of parallelogram ABCD intersect at O as shown in the following fegure. XY contains O, and XY are points on opposite sides of the parallelogram. Give reasons for each of the following:
(i) OB = OD
(ii) ∠OBY = ∠ODX
(iii) ∠BOY = ∠DOX
(iv) ∆BOY ≅ ∆DOX
Now, state if XY is bisected at O. Exercise 17.1 | Q 26 | Page 12

In the following  Figure  ABCD is a  arallelogram, CE bisects ∠C and AF bisects ∠A. In each of the following, if the statement is true, give a reason for the same: (i) ∠A = ∠C
(ii) $\angle FAB = \frac{1}{2}\angle A$

(iii) $\angle DCE = \frac{1}{2}\angle C$

(iv) $\angle CEB = \angle FAB$

(v) CE || AF

Exercise 17.1 | Q 27 | Page 12

Diagonals of a parallelogram ABCD intersect at OAL and CM are drawn perpendiculars to BD such that L and M lie on BD. Is AL = CM? Why or why not?

Exercise 17.1 | Q 28 | Page 12

Points E and F lie on diagonal AC of a parallelogram ABCD such that AE = CF. What type of quadrilateral is BFDE?

Exercise 17.1 | Q 29 | Page 12

In a parallelogram ABCDAB = 10 cm, AD = 6 cm. The bisector of ∠A meets DC in EAEand BC produced meet at F. Find te length CF

Exercise 17.2 [Pages 16 - 17]

### RD Sharma solutions for Class 8 Maths Chapter 17 Understanding Shapes-III (Special Types of Quadrilaterals) Exercise 17.2 [Pages 16 - 17]

Exercise 17.2 | Q 1.01 | Page 16

Which of the following statement is true for a rhombus?

It has two pairs of parallel sides.

Exercise 17.2 | Q 1.02 | Page 16

Which of the following statement is true for a rhombus?

It has two pairs of equal sides.

Exercise 17.2 | Q 1.03 | Page 16

Which of the following statement is true for a rhombus?

It has only two pairs of equal sides.

Exercise 17.2 | Q 1.04 | Page 16

Which of the following statement is true for a rhombus?

Two of its angles are at right angles

Exercise 17.2 | Q 1.05 | Page 16

Which of the following statement is true for a rhombus?

Its diagonals bisect each other at right angles.

Exercise 17.2 | Q 1.06 | Page 16

Which of the following statement is true for a rhombus?

Its diagonals are equal and perpendicular.

Exercise 17.2 | Q 1.07 | Page 16

Which of the following statement is true for a rhombus?

It has all its sides of equal lengths.

Exercise 17.2 | Q 1.08 | Page 16

Which of the following statement is true for a rhombus?

It is a parallelogram.

Exercise 17.2 | Q 1.09 | Page 16

Which of the following statement is true for a rhombus?

Exercise 17.2 | Q 1.1 | Page 16

Which of the following statement is true for a rhombus?

It can be a square.

Exercise 17.2 | Q 1.11 | Page 16

Which of the following statement is true for a rhombus?

It is a square.

Exercise 17.2 | Q 2.1 | Page 17

Fill in the blank, in the following, so as to make the statement true:

A rhombus is a parallelogram in which ......

Exercise 17.2 | Q 2.2 | Page 17

Fill in the blank, inthe following, so as to make the statement true:

A square is a rhombus in which .....

Exercise 17.2 | Q 2.3 | Page 17

Fill in the blank, inthe following, so as to make the statement true:

A rhombus has all its sides of ...... length.

Exercise 17.2 | Q 2.4 | Page 17

Fill in the blank, in the following, so as to make the statement true:

The diagonals of a rhombus ...... each other at ...... angles.

Exercise 17.2 | Q 2.5 | Page 17

Fill in the blank, in each of the following, so as to make the statement true:

If the diagonals of a parallelogram bisect each other at right angles, then it is a ......

Exercise 17.2 | Q 3 | Page 17

The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?

Exercise 17.2 | Q 4 | Page 17

Exercise 17.2 | Q 5 | Page 17

ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.

Exercise 17.2 | Q 6 | Page 17

If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.

Exercise 17.2 | Q 7 | Page 17

Construct a rhombus whose diagonals are of length 10 cm and 6 cm.

Exercise 17.2 | Q 8 | Page 17

Draw a rhombus, having each side of length 3.5 cm and one of the angles as 40°.

Exercise 17.2 | Q 9 | Page 17

One side of a rhombus is of length 4 cm and the length of an altitude is 3.2 cm. Draw the rhombus.

Exercise 17.2 | Q 10 | Page 17

Draw a rhombus ABCD, if AB = 6 cm and AC = 5 cm.

Exercise 17.2 | Q 11 | Page 17

ABCD is a rhombus and its diagonals intersect at O.
(i) Is ∆BOC ≅ ∆DOC? State the congruence condition used?
(ii) Also state, if ∠BCO = ∠DCO.

Exercise 17.2 | Q 12 | Page 17

Show that each diagonal of a rhombus bisects the angle through which it passes.

Exercise 17.2 | Q 13 | Page 17

ABCD is a rhombus whose diagonals intersect at O. If  AB = 10 cm, diagonal BD = 16 cm, find the length of diagonal AC.

Exercise 17.2 | Q 14 | Page 17

The diagonals of a quadrilateral are of lengths 6 cm and 8 cm. If the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral?

Exercise 17.3, Exercise 17.2 [Pages 22 - 23]

### RD Sharma solutions for Class 8 Maths Chapter 17 Understanding Shapes-III (Special Types of Quadrilaterals) Exercise 17.3, Exercise 17.2 [Pages 22 - 23]

Exercise 17.3 | Q 1.01 | Page 22

Which of the following statement is true for a rectangle?

It has two pairs of equal sides.

Exercise 17.3 | Q 1.02 | Page 22

Which of the following statement is true for a rectangle?

It has all its sides of equal length.

Exercise 17.3 | Q 1.03 | Page 22

Which of the following statement is true for a rectangle?

Its diagonals are equal.

Exercise 17.3 | Q 1.04 | Page 22

Which of the following statement is true for a rectangle?

Its diagonals bisect each other.

Exercise 17.3 | Q 1.05 | Page 22

Which of the following statement is true for a rectangle?

Its diagonals are perpendicular.

Exercise 17.3 | Q 1.06 | Page 22

Which of the following statement is true for a rectangle?

Its diagonals are perpendicular and bisect each other.

Exercise 17.3 | Q 1.07 | Page 22

Which of the following statement is true for a rectangle?

Its diagonals are equal and bisect each other.

Exercise 17.3 | Q 1.08 | Page 22

Which of the following statement is true for a rectangle?

Its diagonals are equal and perpendicular, and bisect each other.

Exercise 17.3 | Q 1.09 | Page 22

Which of the following statement is  true for a rectangle?

All rectangles are squares.

Exercise 17.3 | Q 1.1 | Page 22

Which of the following statement is true for a rectangle?

All rhombuses are parallelograms.

Exercise 17.3 | Q 1.11 | Page 22

Which of the following statement is true for a rectangle?

All squares are rhombuses and also rectangles.

Exercise 17.3 | Q 1.12 | Page 22

Which of the following statementis true for a rectangle?

All squares are not parallelograms.

Exercise 17.3 | Q 2.1 | Page 22

Which of the following statement is true for a square?

It is a rectangle.

Exercise 17.3 | Q 2.2 | Page 22

Which of the following statement are true for a square?

It has all its sides of equal length.

Exercise 17.3 | Q 2.3 | Page 22

Which of the following statement  true for a square?

Its diagonals bisect each other at right angle.

Exercise 17.3 | Q 2.4 | Page 22

Which of the following statement  true for a square?

Its diagonals are equal to its sides.

Exercise 17.3 | Q 3.1 | Page 23

Fill in the blank in the following, so as to make the statement true:

A rectangle is a parallelogram in which .....

Exercise 17.3 | Q 3.2 | Page 23

Fill in the blank in  the following, so as to make the statement true:

A square is a rhombus in which .....

Exercise 17.3 | Q 3.3 | Page 23

Fill in the blank of the following, so as to make the statement true:

A square is a rectangle in which .....

Exercise 17.3 | Q 4 | Page 23

A window frame has one diagonal longer than the other. Is the window frame a rectangle? Why or why not?

Exercise 17.3 | Q 5 | Page 23

In a rectangle ABCD, prove that ∆ACB ≅ ∆CAD.

Exercise 17.3 | Q 6 | Page 23

The sides of a rectangle are in the ratio 2 : 3, and its perimeter is 20 cm. Draw the rectangle.

Exercise 17.3 | Q 7 | Page 23

The sides of a rectangle are in the ratio 4 : 5. Find its sides if the perimeter is 90 cm.

Exercise 17.3 | Q 8 | Page 23

Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.

Exercise 17.3 | Q 9 | Page 23

Draw a rectangle whose one side measures 8 cm and the length of each of whose diagonals is 10 cm.

Exercise 17.3 | Q 10 | Page 23

Draw a square whose each side measures 4.8 cm.

Exercise 17.2 | Q 11.1 | Page 23

Identify all the quadrilaterals that have:

Four sides of equal length

Exercise 17.3 | Q 11.2 | Page 23

Identify all the quadrilaterals that have:

Four right angles

Exercise 17.3 | Q 12.1 | Page 23

Explain how a square is a quadrilateral?

Exercise 17.3 | Q 12.2 | Page 23

Explain how a square is  a parallelogram?

Exercise 17.3 | Q 12.3 | Page 23

Explain how a square is a rhombus?

Exercise 17.3 | Q 12.4 | Page 23

Explain how a square is a rectangle?

Exercise 17.3 | Q 13.1 | Page 23

Name the quadrilaterals whose diagonals bisect each other

Exercise 17.3 | Q 13.2 | Page 23

Name the quadrilaterals whose diagonal are perpendicular bisector of each other

Exercise 17.3 | Q 13.3 | Page 23

Name the quadrilaterals whose diagonals are equal.

Exercise 17.3 | Q 14 | Page 23

ABC is a right-angled trianle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from AB and C.

Exercise 17.3 | Q 15 | Page 23

A mason has made a concrete slab. He needs it to be rectangular. In what different ways can he make sure that it is rectangular?

## Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Exercise 17.1Exercise 17.2Exercise 17.3 ## RD Sharma solutions for Class 8 Maths chapter 17 - Understanding Shapes-III (Special Types of Quadrilaterals)

RD Sharma solutions for Class 8 Maths chapter 17 (Understanding Shapes-III (Special Types of Quadrilaterals)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 8 Maths solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Maths chapter 17 Understanding Shapes-III (Special Types of Quadrilaterals) are Properties of Trapezium, Angle Sum Property of a Quadrilateral, Properties of Kite, Classification of Polygons, Properties of a Parallelogram, Concept of Curves, Different Types of Curves - Closed Curve, Open Curve, Simple Curve., Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal, Interior Angles of a Polygon, Exterior Angles of a Polygon and Its Property, Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles, Property: The diagonals of a rhombus are perpendicular bisectors of one another., Properties of Rhombus, Property: The Opposite Sides of a Parallelogram Are of Equal Length., Property: The Opposite Angles of a Parallelogram Are of Equal Measure., Property: The adjacent angles in a parallelogram are supplementary., Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection), Property: The Diagonals of a Rectangle Are of Equal Length., Properties of Rectangle, Properties of a Square, Property: The diagonals of a square are perpendicular bisectors of each other..

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