Question

Very urgent ! How to solve this ?
https://www.dropbox.com/s/u1081lqtcqdbopu/prob%20112.JPG

Answer 1

Can u start the problem somewher?

Answer 2

not able to !

Answer 3

this problem is haunting me. i know there is some simple answer but i just not able to get it.

Answer 4

can you somehow prove AB is parallel to DC ?

Answer 5

how to do that ?

Answer 6

why don't you try?.. try proving PB is parallel to DR (and also equal)

Answer 7

If you view this as a graph with x-y coordinates, then
you can see that the slopes are parallel for the lines. Take the changes in x and y coordinates, which are the lengths.

Answer 8

not able to figure out how ?

Answer 9

If I am not mistaken, points a,b,c,d all connect to make a quadrilateral (specifically) a rhombus. A rhombus is a parallelogram because it has two pairs of parallel lines (making it a parallelogram).

Answer 10

but how can we say that it makes a rhombus ?

Answer 11

I will do it for you.
The two triangles DSR and PQB are congruent by SAS
Let call M the point where PB intersect SR
Angle DRS = angle BPQ = angle PMR
Hence DR is parallel to PB

Answer 12

how to prove AB = DC or the other ?

Answer 13

Yes, two pairs of parallel lines. Look at the dimensions. Slopes are same for each pair.

Answer 14

By the same method, you show that QD is parallel to SB and you are done/

Answer 15

Well the lines are kind of slanted in a rhombus. Look at the vertices of a,b,c,d and then connect them to make a figure.

Answer 16

They are asking only to show that it is a parallelogram

Answer 17

Yes and once you connect the vertices, you can then see that it makes a rhombus which is also a parallelogram.

Answer 18

thanks a lot ! i have got it !

Answer 19

How was your way?

Answer 20

YW

Answer 21

It is not a rhombus in general

Answer 22

eliassaab way helped along with other too !