Square

Q.

The altitude of a right triangle is $7cm$ less than its base. If the hypotenuse is $13cm$, find the other two sides.

Q.

Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle.

Q.

Question 70

The largest square that can be drawn in a circle has a side whose length is 0.707 times the diameter of the circle. By this rule, find the length of the side of such a square, when the diameter of the circle is
(a) 14..5 (b) 8.63

Q.

In the given figure, ABCD is a square and $\angle PQR={90}^{\circ }$. If PB = QC = DR, prove that (i) QB = RC, (ii) PQ = QR, (iii) $\angle QPR={45}^{\circ }$

Q.

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area. [3 MARKS]

Q.

The figure formed by joining the mid-points of the adjacent sides of a square is a

1. square

2. rhombus

3. rectangle

4. parallelogram

Q. Question 4
In quadrilateral ABCD, $\angle A+\angle D={180}^{\circ }$ . What special name can be given to this quadrilateral?

Q.

Find which of the following are true:

1.All rhombuses are squares
2.All squares are rectangles
3.All rectangles are parallelograms
4.All parallelograms are quadrilaterals
5.All parallelograms are rhombuses

1. 2, 3 and 4

2. only 1

3. 1, 2 and 3

4. 3, 4 and 5

Q. ABCD is a cyclic quadrilateral in which AC and BD are it's diagonals. Draw BC as base and AD as upper side respectively. If angle DBC=60 and angle BAC=30, find angle BCD.

Q.

Things which concide with one another are equal to one another. Tell it's meaning with proof to it....!.?..!?..

Q.

K, L, M and N are points on the sides AB, BC, CD and DA respectively of a square ABCD such that AK = BL = CM = DN. Prove that KLMN is a square.

Q. All squares are rectangles but all rectangles are not squares?

1. True
2. False

Q.

The measure of each angles of a convex quadrilateral is _______ $180°$

Q. Question 15
ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.

Q.

A square field is of side $35m$. Find its perimeter and area in acres.

Q.

A metal box with a square base and vertical sides is to contain $1024c{m}^3$. The material for the top and bottom costs $₹5/c{m}^2$ and the material for the sides costs $₹2.50/c{m}^2$. Find the least cost of the box.

Q.

Match the following:

$\begin{array}{cc}\text{Quadrilateral}& \text{Properties}\\ \text{1. Trapezium}& \text{A) A parallelogram, where diagonals bisect at right}\text{angles, all sides are equal and none}\text{of the angles are equal to}{90}^{\circ }\\ \text{2. Square}& \text{B) A quadrilateral, where only one pair}\text{of opposite sides is parallel and unequal}\\ \text{3. Rectangle}& \text{C) A parallelogram, where diagonals are equal,}\text{all sides equal and all the angles are}{90}^{\circ }\\ \text{4. Rhombus}& \text{D) A parallelogram, where diagonals and}\text{opposite sides are equal, and all the angles are}{90}^{\circ }\end{array}$

1. 1 - B, 2 - C, 3 - D, 4 - A

2. 1 - C, 2 - B, 3 - D, 4 - A

3. 1 - C, 2 - B, 3 - A, 4 - D

4. 1 - A, 2 - B, 3 - C, 4 - D

Q. In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes Champa told Chameli, “I think ABCD is a square”. State whether Champa's statement is true or false.

1. True
2. False

Q.

Find the edge of a cube of volume equal to the volume of a cuboid of dimensions 24 cm × 12 cm × 6 cm

1. 6 cm

2. 24 cm

3. 14 cm

4. 12 cm

Q.

A parallelogram with equal sides and equal angles will be:

1. Rectangle

2. Square

3. rhombus

4. Trapezium

Q.

1. DA || DB || DC

2. DA > DB > DC

3. DA = DB = DC

4. DA < DB < DC

Q.

What is the area of a square in $m^2$ with perimeter $128cm?$

Q. Which of the following is not the property of a square?

1. The diagonals of a square bisect each other at right angles.
2. Each angle of a square is a right angle.
3. The diagonals of a square are unequal.
4. The sides of a square are equal.

Q. Which of the following have all sides equal?

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

Q.

ln $△\mathrm{ABC}$, $\mathrm{AD}\perp \mathrm{BC}$ and point $D$ lies on $BC$ such that $2\mathrm{BD}=3\mathrm{CD}$. Prove that $5{\mathrm{AB}}^2=5{\mathrm{AC}}^2+{\mathrm{BC}}^2$.

Q. If PQ and RS are two perpendicular diameters of a circle, then PQRS is a

1. Rectangle
2. Trapezium
3. Square
4. Rhombus but not a square

Q.

ABCD is a rectangle in which diagonal BD bisects $\angle B$. Then, ABCD is a square.

1. True

2. False

Q.

Which of the following set of angles are found in a set squares ?

1. ${30}^{\circ },{60}^{\circ },{90}^{\circ }$

2. ${20}^{\circ },{70}^{\circ },{90}^{\circ }$

3. ${75}^{\circ },{15}^{\circ },{90}^{\circ }$

4. ${45}^{\circ },{45}^{\circ },{90}^{\circ }$

Q.

In the figure, angle ABC = 65^o and angle ACB = 58^o, the measure of angle BDC is

1. 68^o

2. 57^o

3. 90^o

4. 45^o

Q.

All squares are rectangles.

1. True
2. False