In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm.
(i) Write all possible pairs of similar triangles.
(ii) Find the lengths of ME and DM.

Question

In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm. (i) Write all possible pairs of similar triangles. (ii) Find the lengths of ME and DM.

KnowledgeBoat · Accepted Answer

(i) In ΔAME and ΔANC, ⇒ ∠AME = ∠ANC [Since DE || BC so, ME || NC and AN is transversal] ⇒ ∠MAE = ∠NAC [Common angle] ∴ ∆AME ~ ∆ANC [By AA] In ΔADM and ΔABN, ⇒ ∠ADM = ∠ABN [Since DE || BC so, DM || BN and AB is transversal] ⇒ ∠DAM = ∠BAN [Common angle] ∴ ∆ADM ~ ∆ABN [By AA] In ΔADE and ΔABC, ⇒ ∠ADE = ∠ABC [Since DE || BC and AB is transversal] ⇒ ∠AED = ∠ACB [Since DE || BC and AC is transversal] ∴ ∆ADE ~ ∆ABC [By AA] Hence, ∆ADM ~ ∆ABN, ∆AME ~ ∆ANC and ∆ADE ~ ∆ABC. (ii) Since, ∆AME ~ ∆ANC We know that, Corresponding sides of similar triangles are proportional. Since, ∆ADE ~ ∆ABC [Proved above] We know that, Corresponding sides of similar triangles are proportional. ......... (1) Also, ∆ADM ~ ∆ABN [Proved above] Hence, ME = 3.75 cm and DM = 15 cm.

Mathematics

In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm.
(i) Write all possible pairs of similar triangles.
(ii) Find the lengths of ME and DM.

Similarity

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In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm.(i) Write all possible pairs of similar triangles.(ii) Find the lengths of ME and DM.

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(ii) Find the lengths of ME and DM.

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(i) DP : PL = DC : BL.
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(i) CB : BA = CP : PA
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