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