Question

In fig triangle ABC is Similar to triangle MNO, D is the Midpoint of AC and P is the mid point of side MO prove that
1)prove Triangle ABC is similar to triangle MNP
2) BD/NP=AB/MN
(Hint:for similar triangles the ratio of corresponding medians is equals to tge ratio of corresponding sides.)

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Answer 1

Step-by-step explanation:

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Answer 2

In fig triangle ABC is Similar to triangle MNO, D is the Midpoint of AC and P is the mid point of side MO.

• Given,
• Δ ABC ~ Δ MNO
• D is the mid point of AC ⇒ AD = DC
• P is the mid point of MO ⇒ MP = PO
• 1) To prove Δ ABC ~ Δ MNP
• In Δ ABC and Δ MNP
• AB = MN ( given )
• AD = MP ( we have proved above )
• ∠ BDA = ∠NPM  ( angles of congruent sides are equal )
• By SAS theorem, we have,
• Δ ABC ~ Δ MNP
• 2) To prove BD/NP=AB/MN
• as we have already proved that, Δ ABC ~ Δ MNP, we have
• BD = NP (as D and P are the mid-points of similar triangles)
• AB = MN (corresponding sides of similar triangles are same)
• ∴ BD/NP=AB/MN
• (as for similar triangles the ratio of corresponding medians is equals to the ratio of corresponding sides. )