Question

triangles on the same base and between the same parallels

Answer 1

Answer:

Step-by-step explanation:

Are equal because of bpt theorem

Answer 2

Hola dear ☺️❤️

Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Here's the proof⤵️⤵️⤵️

(refer to the attachment for the figure)

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Theorem:
Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Given:
∆ABC and ∆DBC are on the same base BC and between same parallel lines BC and FE.

To prove:
ar(∆ABC) = ar(∆DBC)

Construction:
Draw CE || BA and BF || CD

Proof:

⤵️⤵️

Quadrilateral ABCE is a parallelogram (construction)

and,

Quadrilateral FBCD is also a parallelogram (construction)

Since, ||gm ABCE and ||gm FBCD are on the same base and between the same parallels

Therefore, ar(||gm ABCE) = ar(||gm FBCD) ....... (i)

But AC is the diagonal of ||gm ABCE

Therefore, ar(∆ABC) = ar(∆ACE)

Therefore, ar(∆ABC) = 1/2 ar(||gm ABCE) ....... (ii)

Similarly, we can prove that

ar(∆DBC) = 1/2 ar(||gm FBCD) ....... (iii)

From (i), (ii) and (iii), ar(∆ABC) = ar(∆DBC)

Hence, proved.

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Hope it is helpful to you ✌️✌️