Diagonals of a Square are Perpendicular Bisectors of Each Other

Q. A quadrilateral whose diagonals are equal and bisect each other at right is a

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

Q. PQRS is a square with diagonals PR and SQ meeting at O. Find the value of 'x + 10'.

1. 13

Q. ___ is a quadrilateral whose diagonals are equal and bisect each other at right angles.

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

Q. PQRS is a square with diagonals PR and SQ meeting at O. Find the value of 'x + 10'. [2 Marks]

Q. Match List – I with List – II and select the correct answer using the codes given below the lists:

$\begin{array}{cc}\text{Properties}& \text{Quadrilaterals}\\ \text{In a parallelogram ABCD}& \\ \text{If}\angle D={115}^{\circ }\text{, then the measure of}\angle A\text{=}& {68}^{\circ }\\ \text{PQRS is a square such that PR and SQ intersect at O}& \\ \text{then the measure of}\angle POQ=& {58}^{\circ }\\ \text{The diagonals of a rectangle ABCD meet at O. If}\angle BOC={44}^{\circ }\text{,}& \\ \text{then the measure of}\angle OAD\text{=}& {90}^{\circ }\\ \text{If ABCD is a rectangle with}\angle BAC={32}^{\circ }\text{, then the measure of}& \\ \angle DBC\text{is =}& {65}^{\circ }\end{array}$
Choose the correct option:

1. $\angle A={58}^{\circ },\angle POQ={65}^{\circ },\angle OAD={90}^{\circ },\angle DBC={58}^{\circ }$
2. $\angle A={65}^{\circ },\angle POQ={68}^{\circ },\angle OAD={90}^{\circ },\angle DBC={58}^{\circ }$
3. $\angle A={65}^{\circ },\angle POQ={90}^{\circ },\angle OAD={68}^{\circ },\angle DBC={58}^{\circ }$
4. $\angle A={65}^{\circ },\angle POQ={90}^{\circ },\angle OAD={58}^{\circ },\angle DBC={68}^{\circ }$

Q.

A square is a parallelogram where diagonals bisect each other to form ___.

1. equilateral triangles

2. scalene triangles

3. isosceles triangle with two angles of ${60}^{\circ }$

4. right-angled triangles

Q. ___ is a quadrilateral whose diagonals are equal and bisect each other at right angles.

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

Q. The diagonals of a square intersect at right angles.

1. True
2. False

Q.

In Diagram of the square ACBD, AP = PB = PC. Say True/False.

1. True

2. False

Q. If the diagonals of a quadrilateral intersect perpendicularly then the quadrilateral is square.

1. False
2. True

Q.

If diagonals of a square ACBD intersect at P, then the angle CPB is _______ degrees.

1. 270°

2. 90°
3. 360°
4. 180°