In the trapezium ABCD, AB || DC and AB DC. P and Q are the mid-points of the diagonals AC and BD. Then, PQ || AB and PQ = .....(AB - DC). 1. 2 2. 3 3. 4.

Question

KnowledgeBoat · Accepted Answer

In △BQR and △CQD, ⇒ ∠BQR = ∠CQD (Vertically opposite angles are equal) ⇒ ∠BRQ = ∠QCD (Alternate angles are equal) ⇒ BQ = DQ (Q is the mid-point of BD) ∴ △BQR ≅ △CQD ⇒ BR = DC (Corresponding parts of congruent triangles are equal) ⇒ QR = CQ (Corresponding parts of congruent triangles are equal) Given, AB || DC and PQ || AB ∴ PQ || AB || DC In △ARC, Since, P and Q are the mid-points of AC and CR respectively. By mid-point theorem, ⇒ PQ = AR ⇒ PQ = (AB - BR) ⇒ PQ = (AB - DC) (∵ BR = DC) Hence, option 3 is the correct option.

Mathematics

In the trapezium ABCD, AB || DC and AB DC. P and Q are the mid-points of the diagonals AC and BD. Then, PQ || AB and PQ = .....(AB - DC). 1. 2 2. 3 3. 4.

Mid-point Theorem

Related Questions

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =
4 cm
6 cm
8 cm
10 cm

Mathematics

In the trapezium ABCD, AB || DC and AB DC. P and Q are the mid-points of the diagonals AC and BD. Then, PQ || AB and PQ = .....(AB - DC). 1. 2 2. 3 3. 4.

Mid-point Theorem

Related Questions

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =4 cm6 cm8 cm10 cm

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =
4 cm
6 cm
8 cm
10 cm