Rectangle

Q.

All rectangles are squares, but not vice versa.

1. True

2. False

Q.

The measure of each interior angle of a regular decagon is

1. ${140}^{\circ }$

2. ${100}^{\circ }$

3. ${120}^{\circ }$

4. ${144}^{\circ }$

Q.

Every parallelogram is a rectangle, but not every rectangle is a parallelogram.

1. True

2. False

Q.

All rectangles are parallelograms but all parallelograms are not rectangles justify this statements

Q. Question 2
ABCD is a rhombus and P, Q, R and S are the mid-points of the sides, AB, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Q. Quadrilateral whose diagonals are equal and bisect each other at ${90}^{\circ }$ is known as ______.

1. Rectangle
2. Rhombus
3. Square
4. Parallelogram

Q.

How do you make a quadratic equation with a word problem?

Q.

$ABCD$ is a rhombus with $\angle ABC={56}^{\circ }$. Determine $\angle ACD$.

Q.

The angle between the diagonals of a rectangle is ${90}^{\circ }$.

1. False

2. True

Q.

If ABCD is a parallelogram with two adjacent angles $\angle A=\angle B$ then the parallelogram is a

(a) rhombus

(b) trapezium

(c) rectangle

(d) none of these

Q.

In the following figure ABCD is a trapezium in which $AB\parallel DC$. Find the measure of $\angle C$.

Q.

In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice:

Assertion: If the diagonals of a parallelogram ABCD are equal, then ∠ABC=90°.
Reason: If the diagonals of a parallelogram are equal, it becomes a rectangle.

1. Assertion (A) is true, but reason (R) is false.

2. Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).

3. Assertion (A) is false, but reason (R) is true.

4. Both assertion (A) and reason (R) are true, but reason (R) is the correct explanation of assertion (A).

Q.

The angles of a quadrilateral are in the ratio $2:3:6:7$. The largest angle of quadrilateral is:

1. ${140}^{\circ }$

2. ${160}^{\circ }$

3. ${40}^{\circ }$

4. ${120}^{\circ }$

Q.

The bisectors of the angles of a parallelogram enclose a

(a) rhombus

(b) square

(c) rectangle

(d) parallelogram

Q. All parallelograms are kites.

1. True
2. False

Q. Question 9
The figure obtained by joining the mid-points of the sides of a rhombus, taken In order, is
(A) a rhombus
(B) a rectangle
(C) a square
(D) any parallelogram

Q.

The angles of a quadrilateral are (5x)^o, (3x + 10)^o, (6x – 20)^o and (x + 25)^o. Now, the measure of each angle of the quadrilateral will be

1. 115^o, 79^o, 118^o, 48^o

2. 75^o, 89^o, 128^o, 68^o

3. 100^o, 79^o, 118^o, 63^o

4. 110^o, 84^o, 106^o, 60^o

Q.

Diagonal AC of a parallelogram ABCD bisects angleA then show that it bisects angleC also

Q. If two angles of a rectangle are (x+30)° and (y+50)°, then match the following.

1. 90°
2. 60°
3. 100°
4. 40°

Q.

Prove that the diagonals of a rectangle are equal. [3 MARKS]

Q.

A rectangle is also a parallelogram.

1. True
2. False

Q.

Prove that the opposite angles of a parallelogram are equal.

Q.

A $3\text{m}$ wide path runs outside and around a rectangular park of length $125\text{m}$ and breadth $65\text{m}$. Find the area of the path ?

Q.

If opposite angles of a parallelogram are supplementary, then the parallelogram is _____ .

1. Trapezium
2. Rectangle
3. Rhombus
4. None of the above

Q. Given a rectangle ABCD and P, Q, R, S mid-points of AB, BC, CD and DA respectively. If length of diagonal of rectangle is 8 cm , the quadrilateral PQRS is:

1. Rhombus with side 4 cm
2. Square with side 4 cm
3. Parallelogram with adjacent sides 4 cm and 8 cm
4. Rectangle with adjacent sides 4 cm and 8 cm

Q. Which of the following is not true?

1. Square, rectangle and rhombus are all parallelograms.
2. All rectangles are squares.
3. A parallelogram is a quadrilateral.
4. A kite is not a parallelogram.

Q.

Question 4(ii)
Shade
$\frac{2}{3}$ of the triangles in box

Q. All sides and angles of a square are equal.

1. True
2. False

Q. Sides AB and CD of a quadrilateral ABCD are produced as shown in the following figure. Show that $\angle x+\angle y=\angle a+\angle b$.

Q.

Bisectors of angles of a parallelogram form a

1. Rectangle

2. Trapezium

3. Square

4. Rhombus