Question

solve it fast questions no 15​

Answer 1

Given: A triangle PQR in which RS is a median To prove: ar (∆RPS) = ar (∆RSQ) Construction: Draw RL ⊥ PQ Proof: RS is median ⇒ PS = SQ ⇒ 1 2 12 x PS x RL = 1 2 12 x SQ x RL ⇒ ar (∆RPS) = ar (∆RSQ)Read more on Sarthaks.com - https://www.sarthaks.com/784964/prove-that-a-median-of-a-triangle-divides-it-into-two-triangles-of-equal-area

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Answer 2

Answer:

Let ABC be a triangle and Let AD be one of its medians.

In △ABD and △ADC the vertex is common and these bases BD and DC are equal.

Draw AE⊥BC.

Now area(△ABD)=21×base×altitude of△ADB

=21×BD×AE

=21×DC×AE(∵BD=DC)

but DC and AE is the base and altitude of △ACD

=21× base DC × altitude of △ACD

=area△ACD

⇒area(△ABD)=area(△ACD)

Hence the median of a triangle divides it into two triangles of equal areas.  

Step-by-step explanation:

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