In the given figure, Δ ABC and Δ DEF are similar, BM and EN are their medians. If Δ ABC is similar to Δ DEF, prove that : (i) Δ AMB ∼ Δ DNE (ii) Δ CMB ∼ Δ FNE (iii)

Question

KnowledgeBoat · Accepted Answer

(i) Given, Since, BM and EN are medians of triangles ABC and DEF respectively. ∴ AM = and DN = Given, Δ ABC ∼ Δ DEF ∴ ∠A = ∠D (Corresponding angles of similar triangles are equal) We know that, Corresponding sides of similar triangles are proportional. In Δ AMB and Δ DNE, ⇒ ∠A = ∠D (Proved above) ⇒ [From equation (2)] ∴ Δ AMB ∼ Δ DNE (By SAS postulate) Hence, proved that Δ AMB ∼ Δ DNE. (ii) Given, Since, BM and EN are medians of triangles ABC and DEF respectively. ∴ MC = and NF = Given, Δ ABC ∼ Δ DEF ⇒ ∠C = ∠F (Corresponding angles of similar triangles are equal) Since, corresponding sides of similar triangles are proportional. In Δ CMB and Δ FNE, ⇒ ∠C = ∠F (Proved above) ⇒ [From equation (4)] ∴ Δ CMB ∼ Δ FNE (By SAS postulate) Hence, proved that Δ CMB ∼ Δ FNE. (iii) Given, Δ ABC ∼ Δ DEF We know that, Corresponding sides of similar triangles are proportional. .......(5) Δ AMB ∼ Δ DNE We know that, Corresponding sides of similar triangles are proportional. ......(6) From equation (5) and (6), we get : Hence, proved that .

Mathematics

In the given figure, Δ ABC and Δ DEF are similar, BM and EN are their medians. If Δ ABC is similar to Δ DEF, prove that : (i) Δ AMB ∼ Δ DNE (ii) Δ CMB ∼ Δ FNE (iii)

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Mathematics

In the given figure, Δ ABC and Δ DEF are similar, BM and EN are their medians. If Δ ABC is similar to Δ DEF, prove that : (i) Δ AMB ∼ Δ DNE (ii) Δ CMB ∼ Δ FNE (iii)

Similarity

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