Given : Two triangles ABC and PQR such that (i) ar (∆ABC) = ar(∆PQR) and (ii) AB = PQ.
CN and RT and the altitude corresponding to AB and PQ respectively of the two triangles.
To prove : CR = RT.
Proof: In ∆ABC, CN is the altitude corresponding to the side AB.
ar(∆ABC) = 1/2 AB × CN ....(i)
Similarly, ar(∆PQR) = 1/2 PQ × RT ....(ii)
Since ar(∆ABC) =ar(∆PQR) [Given]
∴ 1/2 AB × CN = 1/2 PQ × RT
Also, AB = PQ [Given]
CN = RT
