Question

Prove that if 2 triangles having the same base and equal areas lie between the same parallels

Answer 1

Theorem: Triangles having the same base and equal areas lie between the same parallels.
Given: DPQR and DSQR such that ar (DPQR) = ar (DSQR).

Construction: Draw PL and SM perpendicular to QR.

To prove: PS || QR

Proof:-we know that,area of a triangle=
1/2 x base x height

therefore, ar(ΔPQR)=
1/2 x QR x PL and ar(ΔSQR) =1/2 x QR xSM

given that ar(ΔPQR) =
ar(ΔSQR)
1/2 x QR x PL=1/2 x QR x SM

==>PL=SM

hence, PS || QR






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