Question

prove that if two angles are on same base and between same parallel lines their areas are equal​

Answer 1

Answer:

Theorem 1: Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Now, suppose ABCD is a parallelogram whose one of the diagonals is AC. Let AN ⊥ DC. Note that

Δ ADC ≅  Δ CBA

So, ar (ADC) = ar (CBA)

Therefore, ar (ADC) = ar (ABDC)

=(DCxAN)

So,area of Δ ADC =× base DC × corresponding altitude AN

In other words, area of a triangle is half the product of its base (or any side) and the corresponding altitude (or height). From this formula, you can see that two triangles with same base (or equal bases) and equal areas will have equal corresponding altitudes.