Theorem 9.3
Two triangles having the same base (or equal bases) and equal areas lie between the same parallels. Let us now take some examples to illustrate the use of the above results.
Given : ABC and ABD are two triangles
on same base AB such that
r ( ABC) = r ( ABD).
Join CD
To Prove : CD AB
Construction : Draw the altitudes of ABC and ABD through C and D and meeting base at E and F respectively
Proof:
Since CE AB & DF AB
Since, lines perpendicular to same line are parallel to each other.
CE DF
Now,
Since r ( ABC) = r ( ABD)
CF = DF
Now,
In CDFE,
CE DF & CE = DF
Since one pair of opposite sides is equal and parallel
Hence, CDFE is parallelogram
So, CD EF
CD AB
Hence, Proved

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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