Question

Triangle ABC is similar to triangle MNP ( Δ ABC ~ Δ MNP) What is the value of x?

Answer 1

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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. )

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Answer 2

Answer:

x=12

Step-by-step explanation:

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