Rhombus

Q.

Prove that the diagonals of a rectangle are of equal length.

Q.

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

Q.

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

Q. Question 110
State whether the statements are True or False.
Diagonals of a rhombus are equal and perpendicular to each other.

Q.

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hand to talk to each other. Find the length of the string of each phone.

1. 20√3

2. 40√3

3. 30√3

4. 10√3

Q.

The length of the two diagonals of a rhombus are $6cm$ and $8cm$ respectively, what is the length of its side.

Q.

The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively. Find the length of each of its sides.

Q. If AOB is a diameter of the circle and AC = BC, then $\angle CAB$ is equal to:

1. 
2. 
3. 
4. 

Q.

ABCD is a rhombus whose diagonals intersect at 0. If AB = 10 cm, diagonal BD = 16 cm, find the length of diagonal AC.

Q.

The two diagonals are not necessarily equal in a

(a) rectangle (b) square

(c) rhombus (d) isoceles trapezium

Q.

Name a quadrilateral whose all angles are equal to $\text{90°}$.

Q. 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.

Q.

$\text{ABCD is a rhombus. if}\angle BCA={35}^{\circ },find\angle ADC.$

Q.

Question 75

Find the length of the largest pole that can be placed in a room of dimensions $12m\times 4m\times 3m$.

Q.

A parallelogram is called a square of all of its sides are equal.

1. True

2. False

Q.

Name each of the following parallelograms :

(i) The diagonals are equal and the adjacent sides are unequal.

(ii) The diagonals are equal and the adjacent sides are equal.

(iii) The diagonals are unequal and the adjacent sides are equal.

(iv) All the sides are equal and one angle is ${60}^{\circ }$

(v) All the sides are equal and one angle is ${90}^{\circ }$

(vi) All the angles are equal and the adjacent sides are unequal.

Q. If adjacent sides of a parallelogram are equal, then it is a .

1. trapezium
2. rhombus
3. triangle
4. rectangle

Q.

Construct the following quadrilateral: Rhombus $\text{BEND. BN = 5.6 cm, ED = 6.5 cm}$

Q. Measure of one angle of a rhombus is 50$°$. find the measures of remaining three angles.

Q.

The diagonals do not necessarily intersect at right angles in a

(a) parallelogram

(b) rectangle

(c) rhombus

(d) kite

Q. Which of the following statements are true for both square and rhombus?
1. All the sides are congruent.
2. All the angles are congruent.
3. Diagonals are congruent.
4. Diagonals are perpendicular bisectors.

1. 2 and 3 only
2. 1, 2 and 4 only
3. 1 and 3 only
4. 1 and 4 only

Q. Question 121
State whether the statements are True or False.
Every rhombus is a trapezium.

Q.

$\text{ABCD is a rhombus. if}\angle BAC={38}^{\circ },find:\left(i\right)\angle ACB\left(ii\right)\angle DAC\left(iii\right)\angle ADC.$

Q.

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

Q.

Make Sentence.

( Use: All, Some, No to complete the sentence. )\\

________________ parallelograms are quadrilaterals.

Q.

ABCD is a rhombus and its diagonals intersect at O.

(i) Is $\Delta BOC\cong \Delta DOC$? State the congruence condition used?
(ii) Also state, if $\angle BCO=\angle DCO$.

Q.

$\text{The given figure shows a rhombus ABCD in which angle}BCD={180}^{\circ }.\text{Find angle s x and y.}$

Q. Which of the following statements are true for a rhombus.

x. It can be a square.

Q. OABC is a rhombus. Find $m\angle AOC$

Q.

Construct a rectangle ABCD whose one side BC = 4.5 cm and diagonal AC = 6 cm [3 MARKS]