Parallelograms on the Same Base and between the Same Parallel Lines – Part 2

# Parallelograms on the Same Base and between the Same Parallel Lines – Part 2

• Parallelograms On the Same Base and Between the Same Parallel Lines
• Summary
• What’s Next?

In the previous segment, we had a brief introduction to figures on the same base and between the same parallel lines. In this segment, we understand why these figures have the same area.

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## Parallelograms On the Same Base and Between the Same Parallel Lines

Parallelograms on the same base and between the same parallels are equal in area.

Consider two parallelograms ABCD and PQCD, on the same base DC and between the same parallels AQ and DC. Figure 1

 1 In △ADP and △BCQ, ∠DAP = ∠CBQ Corresponding angles from AD || BC and transversal AQ 2 In △ADP and △BCQ, ∠DPA = ∠CQB Corresponding angles from DP || CQ and transversal AQ 3 Side AD ≅ Side BC Opposite sides of a parallelogram are equal 4 ∴ △ADP ≅ △BCQ AAS test of congruency 5 ∴ Area(△ADP) = Area(△BCQ) Congruent figures have equal areas

## Related content

 AREAS OF PARALLELOGRAMS AND TRIANGLESCongruent Figures Parallelograms on the Same Base and between the Same Parallel Lines – Part 1 A Triangle and a Parallelogram on the Same Base between the Same Parallel Lines Triangles Having The Same Base And Between The Same Two Parallel Lines Triangles having the same base and between the same two parallels – Converse  +91

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