# Parallelograms Diagonal Properties Free Doubts and Solutions

### CBSE - IX - Mathematics - Quadrilaterals

## Diagonal AC of a parallelogram ABCD bisects angle A. (a) Does angle A bisects angle c also? Give reasons. (b) Is AbCD a rhombus? Give reasons.

**kirtiagarwal148**18th February 2018, 9:39 PM

### CBSE - IX - Mathematics - Quadrilaterals

## 1. Show that the diagonals of a Square are equal and bisect each other at right angles.
2. If the diagonals of a quardilateral are equal and bisect each other at rigjt angles, then show that its a square.

**Jitendra**26th September 2017, 4:35 PM

### CBSE - IX - Mathematics - Quadrilaterals

## PQRS is a square. PR and SQ intersect at O. What is the measure of POQ?

**Topperlearning User**17th August 2017, 7:45 AM

### CBSE - IX - Mathematics - Quadrilaterals

## Prove that the diagonals of a rhombus are perpendicular to each other.

**Topperlearning User**17th August 2017, 7:45 AM

### CBSE - IX - Mathematics - Quadrilaterals

## ABCD is a rhombus ABC = 66o. Determine ACD.

**Topperlearning User**17th August 2017, 7:41 AM

### CBSE - IX - Mathematics - Quadrilaterals

## The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus.

**Topperlearning User**17th August 2017, 7:30 AM

### CBSE - IX - Mathematics - Quadrilaterals

## ABCD is a square prove that diagonal BD bisects B as well as D.

**Topperlearning User**17th August 2017, 7:29 AM

### CBSE - IX - Mathematics - Quadrilaterals

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

**Topperlearning User**17th August 2017, 7:25 AM

### CBSE - IX - Mathematics - Quadrilaterals

## PQRS is a parallelogram and X and Y are points on the diagonal QS such that SX = QY. Prove that PXRY is a parallelogram.

**Topperlearning User**17th August 2017, 7:24 AM

### CBSE - IX - Mathematics - Quadrilaterals

## Show that the line segments joining the mid points of the opposite sides of a quadrilateral bisect each other.

**Topperlearning User**17th August 2017, 7:23 AM

### CBSE - IX - Mathematics - Quadrilaterals

## Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Find the length of the other diagonal and hence find the area of the rhombus.

**Topperlearning User**17th August 2017, 7:22 AM

### CBSE - IX - Mathematics - Quadrilaterals

##
Prove that the diagonals of a parallelogram divides it into two congruent triangles

Prove that the diagonals of a parallelogram divides it into two congruent triangles

**Paresh**11th December 2015, 2:59 PM

### CBSE - IX - Mathematics - Quadrilaterals

##
ABCD is a rectangle in which diagonal BD bisects <B. Show that ABCD is a square

ABCD is a rectangle in which diagonal BD bisects <B. Show that ABCD is a square

**Paresh**11th December 2015, 2:32 PM

### CBSE - IX - Mathematics - Quadrilaterals

##
In a parallelogram ABCD, E and F are the midpoints of sides AB and CD. Prove that the line segments AF and CE trisect the diagonal BD

In a parallelogram ABCD, E and F are the midpoints of sides AB and CD. Prove that the line segments AF and CE trisect the diagonal BD

**Paresh**11th December 2015, 1:38 PM

### CBSE - IX - Mathematics - Quadrilaterals

## my doubt is if there is a rhombus ABCD and we draw a diagnol AC will this diagnol bisect angles A and C.

**kiranq6**12th November 2015, 9:59 AM

### CBSE - IX - Mathematics - Quadrilaterals

##
The value of x in the given parallelogram is

**buntitanooj**25th October 2015, 2:20 PM

### CBSE - IX - Mathematics - Quadrilaterals

5. In a cyclic quadrilateral PQRS If angle P - angle R = 50 degrees. Find the measure of angle P and angle R

5. In a cyclic quadrilateral PQRS If angle P - angle R = 50 degrees. Find the measure of angle P and angle R

**avantikadandapani**17th November 2014, 6:36 PM

### CBSE - IX - Mathematics - Quadrilaterals

Two parallel l and m are intersected by transversal P . Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

Two parallel l and m are intersected by transversal P . Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

**avantikadandapani**17th November 2014, 6:16 PM

### CBSE - IX - Mathematics - Quadrilaterals

## the lengths of the diagonal of a rhombus are 24 cm and 18 cm respectively. find the length of each side of the rhombus

**dev**10th November 2014, 8:26 PM

### CBSE - IX - Mathematics - Quadrilaterals

**TEO PARALLELOGAMS HAVE A COMMON DIAGONAL SHOW THAT THE ANGULAR POINTS ARE THOSE OF A PARALLELOGRAM.**

**TEO PARALLELOGAMS HAVE A COMMON DIAGONAL SHOW THAT THE ANGULAR POINTS ARE THOSE OF A PARALLELOGRAM.****M.s.srinidhi21**6th October 2014, 7:40 AM

### CBSE - IX - Mathematics - Quadrilaterals

##
*IN A PARALLELOGRAM ABCD THE BISECTORS OFANGLE A ALSO BISECTS BC AT X.PROVE THAT AD=2AB*

*IN A PARALLELOGRAM ABCD THE BISECTORS OFANGLE A ALSO BISECTS BC AT X.PROVE THAT AD=2AB*

**M.s.srinidhi21**6th October 2014, 7:02 AM

### CBSE - IX - Mathematics - Quadrilaterals

##
**IF PQRS IS A PARALLELOGRAM,PQ AND QO ARE,RESPECTIVELY THE ANGLE BISECTS OF ANGLE P AND ANGLE Q.LINE LOM IS DRAWN PARALLEL TO PQ.PROVE THAT**

**1. PL=QM**

**2. LO=OM**

**IF PQRS IS A PARALLELOGRAM,PQ AND QO ARE,RESPECTIVELY THE ANGLE BISECTS OF ANGLE P AND ANGLE Q.LINE LOM IS DRAWN PARALLEL TO PQ.PROVE THAT**

**1. PL=QM**

**2. LO=OM**

**M.s.srinidhi21**6th October 2014, 6:57 AM

### CBSE - IX - Mathematics - Quadrilaterals

## Show that the diagonals of a rhombus are perpendicular to each other.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## Diagonal AC of a parallelogram bisects A. Show that: (i) it bisects C also (ii) ABCD is a rhombus

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## D, E and F respectively are the mid-points of the sides BC, CA and AB of ABC. Show that ar(DEF) =

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## Diagonals of a parallelogram ABCD intersect at point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## Show that diagonals of a square are equal and bisect each other at right angles.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Quadrilaterals

## ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersect AB at P and DC at Q. Prove that: ar(POA) = ar(QOC)

**Topperlearning User**10th December 2013, 10:02 AM