Question

geometry ques..
image coming up..

Answer 1

@eliassaab @mukushla @ganeshie8

Answer 2

Is this from the Entrance Examination for CMI BSc (Mathematics & Computer Science) May 2011from the Chennai Mathematical Institute?

http://www.cmi.ac.in/admissions/sample-qp/ugmath2011.pdf ?

Answer 3

yes..am aiming for it next year..

Answer 4

There are some interesting questions on there. I wish you the best of luck, it's good that you're preparing now! :)

Answer 5

yes,,altough most questions werent that difficult..but true,nice bunch of problems..

Answer 6

Since the opposite angles are right angles the quadrilateral can either be a square or a rectangle.The proof is in the picture.

Answer 7

And AAS congruency rule is Angle Angle side that is if the corresponding two angles and side of two triangles are equal they are said to be congruent.

Answer 8

buddy that assumption is wrong,, 2 angles 90 doesnt mean other 2 will also be 90

Answer 9

this can be concluded though ,since opposite angles 90,,i.e. sum to 180,,its a cyclic quad,,not so sure if that'd help..

Answer 10

If the angles are not opposite the assumption is wrong but they are opposite bro.They can only be 90 degrees.

Answer 11

These triangles share a hypotenuse. You can stitch together two 3,4,5 triangles such that they share the hypotenuse, but the 3 and 4 are adjacent, not opposite.

Answer 12

well how about this :

which is exactly what @mathteacher1729 says..

Answer 13

anyways,,i have got the solution..thanks all for the efforts by the way..hold on,,i'll post the solution..

Answer 14

I called my maths teacher and verified it.He says its right.

Answer 15

let AM=m , CN=n , DM=a , MN=b , NB =c
<ADM> = y and <ABM>=x
now <CDN>=90-y
=> <DCN> = y
also <CBM>=90-x
=> <NCB>=x
tan x = m/(b+c) = c/n
tany = m/a = (a+b)/n
from these 2 eqns ,we have
mn = c(b+c) = a(a+b)
=> (b+c)/(a+b) = a/c ......eqn (1)

subtracting 1 from both sides in eqn(1) ,,
=>(c-a)/(a+b) =(a-c)/(a+c)
=> (c-a)(a+c) = (a-c)(a+b)
=>(c-a)(a+c) - (a-c)(a+b) =0
=>(c-a)(a+c+a+b) =0
well 2a+b+c is ofcorse not equal to 0
only thing which can be 0 here is c-a

this c-a=0
or c=a..
hence proved!!
phew!

Answer 16

lol i missed the fig,,1 min.,,