In a parallelogram A B C D , ∠ A is 1 4 of ∠ B . Find ∠ C and ∠ D

In the given parallelogram A B C D , ∠ A = 1 4 ∠ B We know that the adjacent angles of a parallelogram are supplementary ∴ ∠ A + ∠ B = 180 ° ⇒ 1 4 ∠ B + ∠ B = 180 ° ⇒ 5 4 ∠ B = 180 ° ⇒ ∠ B = 180 ° × 4 5 = 144 ° ∴ ∠ A = 1 4 ∠ B = 1 4 × 144 ° = 36 ° We know that in a parallelogram, opposite angles are equal ∴ ∠ C = ∠ A = 36 ° and ∠ D = ∠ B = 144 °

In the adjacent figure, P Q R S is a rhombus. If O R = 4 cm and O S = 3 cm , find the length of S R .

A rhombus is a special case of parallelogram with all sides equal. Rhombus is having two diagonals which bisect each other perpendicularly, dividing the rhombus into four right-angled triangles. ∴ △ S O R is a right-angled triangle Then, by Pythagoras theorem, S R 2 = O R 2 + O S 2 Given O R = 4 cm and O S = 3 cm That is, S R 2 = 4 2 + 3 2 ⇒ S R = 16 + 9 = 5 cm Therefore, S R = 5 cm

In the adjacent figure, P Q R S is a rhombus. Find the perimeter of the given rhombus.

A rhombus is a special case of parallelogram with all sides equal. Rhombus is having two diagonals which bisect each other perpendicularly, dividing the rhombus into four right-angled triangles. ∴ △ S O R is a right angled triangle. Then, by Pythagoras theorem, ⇒ S R = 16 + 9 = 5 cm As all the sides of a rhombus are equal, Perimeter of a rhombus = 4 × side = 4 × 5 cm = 20 cm Therefore, Perimeter of a rhombus is 20 cm .

E M B I B E

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 1

MEDIUM

8th CBSE

IMPORTANT

Earn 100

In a parallelogram, if for any adjacent angles, the measure of one of its angles is four times that of the other, find the measures of the angles of the parallelogram.

Important Questions on Properties of Quadrilaterals

HARD

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 2

In the adjacent figure, find each angle marked with a letter.
Question Image

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 3

In a parallelogram

A B C D

,

∠ A

is

\frac{1}{4}

of

∠ B

. Find

∠ C

and

∠ D

EASY

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 4

In the adjacent figure,

P Q R S

is a rhombus. Consider

△ R O S

. What kind of triangle is

△ R O S

?

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 4

In the adjacent figure,

P Q R S

is a rhombus.
Question Image

If

O R = 4 cm

and

O S = 3 cm

, find the length of

S R

.

EASY

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 4

In the adjacent figure,

P Q R S

is a rhombus.
Question Image

Find the perimeter of the given rhombus.

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 5

In the given figure,

A B C D

is a parallelogram, the bisectors of consecutive angles

∠ A

and

∠ B

intersect at

L

. Show that

∠ A L B = 90^{o}

HARD

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 6

The diagonals of a quadrilateral are perpendicular to each other. Show that the quadrilateral formed by joining the midpoints of its sides is a rectangle.

HARD

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 15 - Properties of Quadrilaterals>Revision Time>Q 7

In the given figure, the sides