Prove that the area of a quadrilateral between a base and parallel lines is equal.​

Question

Prove that the area of a quadrilateral between a base and parallel lines is equal.​

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Iris 2 months 2021-09-10T17:50:35+00:00 1 Answer 0 views 0

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    2021-09-10T17:51:54+00:00

    Answer:

    Here we will prove that parallelogram on the same base and between the same parallel lines are equal in area.

    Given: PQRS and PQMN are two parallelograms on the same base PQ and between same parallel lines PQ and SM.

    To prove: ar(parallelogram PQRS) = ar(parallelogram PQMN).

    Construction: Produce QP to T.

    Proof:

    Statement Reason

    1. PS = QR. 1. Opposite sides of the parallelogram PQRS.

    2. PN = QM. 2. Opposite sides of the parallelogram PQMN.

    3. ∠SPT = ∠RQT. 3. Opposite sides PS and QR are parallel and TPQ is a transversal.

    4. ∠NPT = ∠MQT. 4. Opposite sides PN and QM are parallel and TPQ is a transversal.

    5. ∠NPS = ∠MQR. 5. Subtracting statements 3 and 4.

    6. ∆PSN ≅ ∆RQM 6. By SAS axiom of congruency.

    7. ar(∆PSN) ≅ ar(∆RQM). 7. By area axiom for congruent figures.

    8. ar(∆PSN) + ar(quadrilateral PQRN) = ar(∆RQM) + ar(quadrilateral PQRN) 8. Adding the same area on both sides of the equality in statement 7.

    9. ar(parallelogram PQRS) = ar(parallelogram PQMN). (Proved) 9. By addition axiom for area.

    Step-by-step explanation:

    MARK AS ME BRILLIANT

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