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Home » In the given figure, CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC ~ ∆PQR, prove that: (i) ∆AMC ~ ∆PQR (ii) CM/RN = AB/PQ (iii) ∆CMB ~ ∆RNQ
In the given figure, CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC ~ ∆PQR, prove that:
(i) ∆AMC ~ ∆PQR
(ii) CM/RN = AB/PQ
(iii) ∆CMB ~ ∆RNQ
CBSE | Class 10 | Maths | ML Aggarwal | Similarity
In the given figure, CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC ~ ∆PQR, prove that:
(i) ∆AMC ~ ∆PQR
(ii) CM/RN = AB/PQ
(iii) ∆CMB ~ ∆RNQ

Solution:-

From the given figure it is given that, CM and RN are respectively the medians of ∆ABC and ∆PQR.

(i) We have to prove that, ∆AMC ~ ∆PQR

Consider the ∆ABC and ∆PQR

As ∆ABC ~ ∆PQR

∠A = ∠P, ∠B = ∠Q and ∠C = ∠R

And also corresponding sides are proportional

AB/PQ = BC/QR = CA/RP

Then, consider the ∆AMC and ∆PNR,

∠A = ∠P

AC/PR = AM/PN

Because, AB/PQ = ½ AB/½PQ

AB/PQ = AM/PN

Therefore, ∆AMC ~ ∆PNR

(ii) From solution(i) CM/RN = AM/PN

CM/RN = 2AM/2PN

CM/RN = AB/PQ

(iii)Now consider the ∆CMB and ∆RNQ

∠B = ∠Q

BC/QP = BM/QN

Therefore, ∆CMB ~ ∆RNQ

i

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