#### Chapters

Chapter 2: Powers

Chapter 3: Squares and Square Roots

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Algebraic Expressions and Identities

Chapter 7: Factorization

Chapter 8: Division of Algebraic Expressions

Chapter 9: Linear Equation in One Variable

Chapter 10: Direct and Inverse Variations

Chapter 11: Time and Work

Chapter 12: Percentage

Chapter 13: Proft, Loss, Discount and Value Added Tax (VAT)

Chapter 14: Compound Interest

Chapter 15: Understanding Shapes-I (Polygons)

Chapter 16: Understanding Shapes-II (Quadrilaterals)

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

Chapter 18: Practical Geometry (Constructions)

Chapter 19: Visualising Shapes

Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)

Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Chapter 23: Data Handling-I (Classification and Tabulation of Data)

Chapter 24: Data Handling-II (Graphical Representation of Data as Histograms)

Chapter 25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

Chapter 26: Data Handling-IV (Probability)

Chapter 27: Introduction to Graphs

#### RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

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

#### RD Sharma solutions for Class 8 Maths Chapter 17 Exercise 17.1 [Pages 9 - 12]

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

(i) *AD* =

(ii) ∠*DCB* =

(iii) *OC* =

(iv) ∠*DAB* + ∠*CDA* =

The following figure is parallelogram. Find the degree values of the unknowns *x*, *y*, *z*.

The following figure is parallelogram. Find the degree values of the unknown *x*, *y*, *z*.

The following figure is parallelogram. Find the degree values of the unknown *x*, *y*, *z*.

The following figure is parallelogram. Find the degree values of the unknown *x*, *y*, *z*.

The following figure is parallelogram. Find the degree values of the unknown *x*, *y*, *z*.

The following figure is parallelogram. Find the degree value of the unknown *x*, *y*, *z*.

Can the following figure be parallelogram. Justify your answer.

Can the following figure be parallelogram. Justify your answer.

Can the following figure be parallelogram. Justify your answer.

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.

In the following figure *GUNS* and *RUNS* are parallelogram. Find *x* and *y*.

In the following figure *GUNS* and *RUNS* are parallelogram. Find *x* and *y*.

In the following figure *RISK* and *CLUE* are parallelograms. Find the measure of *x*.

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

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

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

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

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

*ABCD* is a parallelogram in which ∠*A** = *70°. Compute ∠*B**, *∠*C** *and* *∠*D**.*

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

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?

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

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.

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.

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

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*.

Find the angles marked with a question mark shown in Fig. 17.27

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.

In the following figure, *ABCD* and *AEFG* are parallelograms. If ∠*C* = 55°, what is the measure of ∠*F*?

In the following figure, *BDEF* and *DCEF* are each a parallelogram. Is it true that *BD* = *DC*? Why or why not?

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

Diagonals of parallelogram *ABCD* intersect at *O* as shown in the following fegure. *XY* contains *O*, and *X*, *Y* 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*.

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 *

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

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

In a parallelogram *ABCD*, *AB* = 10 cm, *AD* = 6 cm. The bisector of ∠*A* meets *DC* in *E*, *AE*and *BC* produced meet at *F*. Find te length *CF*.

#### RD Sharma solutions for Class 8 Maths Chapter 17 Exercise 17.2 [Pages 16 - 17]

Which of the following statement is true for a rhombus?

It has two pairs of parallel sides.

Which of the following statement is true for a rhombus?

It has two pairs of equal sides.

Which of the following statement is true for a rhombus?

It has only two pairs of equal sides.

Which of the following statement is true for a rhombus?

Two of its angles are at right angles

Which of the following statement is true for a rhombus?

Its diagonals bisect each other at right angles.

Which of the following statement is true for a rhombus?

Its diagonals are equal and perpendicular.

Which of the following statement is true for a rhombus?

It has all its sides of equal lengths.

Which of the following statement is true for a rhombus?

It is a parallelogram.

Which of the following statement is true for a rhombus?

It is a quadrilateral.

Which of the following statement is true for a rhombus?

It can be a square.

Which of the following statement is true for a rhombus?

It is a square.

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

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

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

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

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

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

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

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

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 ......

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

The diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? If your answer is 'No', draw a figure to justify your answer.

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

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

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

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

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

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

*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*.

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

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

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?

#### RD Sharma solutions for Class 8 Maths Chapter 17 Exercise 17.3, 17.2 [Pages 22 - 23]

Which of the following statement is true for a rectangle?

It has two pairs of equal sides.

Which of the following statement is true for a rectangle?

It has all its sides of equal length.

Which of the following statement is true for a rectangle?

Its diagonals are equal.

Which of the following statement is true for a rectangle?

Its diagonals bisect each other.

Which of the following statement is true for a rectangle?

Its diagonals are perpendicular.

Which of the following statement is true for a rectangle?

Its diagonals are perpendicular and bisect each other.

Which of the following statement is true for a rectangle?

Its diagonals are equal and bisect each other.

Which of the following statement is true for a rectangle?

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

Which of the following statement is true for a rectangle?

All rectangles are squares.

Which of the following statement is true for a rectangle?

All rhombuses are parallelograms.

Which of the following statement is true for a rectangle?

All squares are rhombuses and also rectangles.

Which of the following statementis true for a rectangle?

All squares are not parallelograms.

Which of the following statement is true for a square?

It is a rectangle.

Which of the following statement are true for a square?

It has all its sides of equal length.

Which of the following statement true for a square?

Its diagonals bisect each other at right angle.

Which of the following statement true for a square?

Its diagonals are equal to its sides.

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

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

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

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

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

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

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

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

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

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

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

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

Draw a square whose each side measures 4.8 cm.

Identify all the quadrilaterals 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 diagonal are perpendicular bisector of each other

Name the quadrilaterals whose diagonals are equal.

*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 *A*, *B* and *C*.

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)

#### RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

## RD Sharma solutions for Class 8 Mathematics 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 Mathematics for Class 8 by R D Sharma (2019-2020 Session) 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 Mathematics chapter 17 Understanding Shapes-III (Special Types of Quadrilaterals) are Regular and Irregular Polygons, Angle Sum Property, Sum of the Measures of the Exterior Angles of a Polygon, Concept of Trapezium, Concept of Kite, Elements of a Parallelogram, Diagonals of a Parallelogram, Concept of Rhombus, Concept of a Rectangle, Classification of Polygons, Concept of Diagonals, Convex and Concave Polygons, Introduction of Quadrilaterals, Concept of a Square, Concept of Parallelogram.

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