Question

parallelograms on the same base and between the same parallels are equal in area

Answer 1

yes
it is theorem 9.1

Draw a parallelogram ABCD on a thick sheet of paper or a cardboard sheet.

Now, draw a line segment DE as shown in the figure.

Next, cut a triangle A’D’E’ congruent to triangle ADE in a separate sheet with the help of a tracing paper and place ∆ A’D’E’ in such a way that A’D’ coincides with BC as shown in adjoining figure

Note that there are two parallelograms ABCD and EE’CD on the same base DC and between the same parallels AE’ and DC. What can you say about their areas?

As                                       ∆ADE ≅ ∆ A’ D’ E’

Therefore                             Area (ADE) = Area (A’ D’ E’)

Also                                    Area (ABCD) = Area (ADE) + Area (EBCD)

                                                             = Area (A’D’E’) + Area (EBCD)

                                                             = Area (EE’CD)

So, the two parallelograms are equal in area.

Answer 2

Solution is in photo
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