Sides AB, BC and median AD of the triangle ABC are respectively proportional to sides PQ, QR and median PM of triangle PQR.
Prove that:
(i) Δ ABD ∼ Δ PQM
(ii) Δ ABC ∼ Δ PQR

Question

Sides AB, BC and median AD of the triangle ABC are respectively proportional to sides PQ, QR and median PM of triangle PQR. Prove that: (i) Δ ABD ∼ Δ PQM (ii) Δ ABC ∼ Δ PQR

KnowledgeBoat · Accepted Answer

(i) Given, AB, BC and median AD of the triangle ABC are respectively proportional to sides PQ, QR and median PM of triangle PQR. AD is median of triangle ABC. ∴ BD = DC = BC PM is median of triangle PQR. ∴ QM = RM = QR In Δ ABD and Δ PQM, ∴ Δ ABD ∼ Δ PQM (By SSS postulates) Hence, Δ ABD ∼ Δ PQM. (ii) From (i), Δ ABD ∼ Δ PQM Corresponding angles of similar triangles are equal. ∴ ∠ABD = ∠PQM ................(1) In Δ ABC and Δ PQR, ⇒ ∠ABC = ∠PQR [From equation (1)] ∴ Δ ABC ∼ Δ PQR (By SAS postulate) Hence, Δ ABC ∼ Δ PQR.

Mathematics

Sides AB, BC and median AD of the triangle ABC are respectively proportional to sides PQ, QR and median PM of triangle PQR.
Prove that:
(i) Δ ABD ∼ Δ PQM
(ii) Δ ABC ∼ Δ PQR

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Mathematics

Sides AB, BC and median AD of the triangle ABC are respectively proportional to sides PQ, QR and median PM of triangle PQR.Prove that:(i) Δ ABD ∼ Δ PQM(ii) Δ ABC ∼ Δ PQR

Similarity

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Sides AB, BC and median AD of the triangle ABC are respectively proportional to sides PQ, QR and median PM of triangle PQR.
Prove that:
(i) Δ ABD ∼ Δ PQM
(ii) Δ ABC ∼ Δ PQR