Yes it is, Avinash – if you notice, in the proof, we have not made any assumptions about the non-parallel sides; they could be equal or not, it doesn’t matter.
Think about it for a moment… Area = 1/2 * base * height. So if the heights are the same (as is the case here) area will be proportional to the base, correct?
Just go the Euclid way. Start with points/lines/planes and prove your way upwards through triangles, quads, polygons, circles and 3-D stuff. (Prove everything to yourself, else you won’t be able to apply it) Take a detour though trigo and co-geo at some point.
As to the latter query: possible, yes; easy, no. You might end up settling for something less than what you are capable of. I am assuming you have already filled the form, or else the question is moot 🙂 If you are already very strong in either English or Maths, go for it seriously; if you are moderate at best in both, then take 18 just for the experience and plan for 19 as the serious attempt.
CAT-holics 
Is this funda applicable to both Normal Trapezium and Isosceles Trapezium? Plz reply…
Yes it is, Avinash – if you notice, in the proof, we have not made any assumptions about the non-parallel sides; they could be equal or not, it doesn’t matter.
regards
J
Hello Sir,
Kindly please explain how we got the ratio of areas of two similar triangles as p^2 : q^2
Standard result for any two similar figures. See the post on similarity of triangles.
regards
J
Can you please help me with the flow of studying “Geometry” for CAT. Am confused as i started with Trapezium.
How should i move step by step?
In 15 days? All I can say is “Good Luck”.
regards
J
May i know which theorem is used for comparing AOB and AOD.How is their ratio are in p:q could you explain.
Think about it for a moment… Area = 1/2 * base * height. So if the heights are the same (as is the case here) area will be proportional to the base, correct?
regards
J
Hi J, Please help me with the flow of Geometry. Also wanted your suggestion if CAT 2018 is possible starting October for a CA
Just go the Euclid way. Start with points/lines/planes and prove your way upwards through triangles, quads, polygons, circles and 3-D stuff. (Prove everything to yourself, else you won’t be able to apply it) Take a detour though trigo and co-geo at some point.
As to the latter query: possible, yes; easy, no. You might end up settling for something less than what you are capable of. I am assuming you have already filled the form, or else the question is moot 🙂 If you are already very strong in either English or Maths, go for it seriously; if you are moderate at best in both, then take 18 just for the experience and plan for 19 as the serious attempt.
regards
J