Question

APOR-AABC and PQ AB= 2: 5, If PM and AN are the medians, then find the ratio of their corresponding medians, ​

Answer 1

Answer:

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Answer 2

Given:

Δ PQR ~ Δ ABC and PQ AB= 2: 5, If PM and AN are the medians, then find the ratio of their corresponding medians.

To find:

​The ratio of their corresponding medians

Solution:

We know that,

If any two triangles are similar, then their corresponding medians are proportional to their corresponding sides.

Here we have,

Δ PQR and Δ ABC are similar triangles.

PQ : AB = 2 : 5 . . . (1)

PM is the median of Δ PQR

AN is the median of Δ ABC

Now, based on the above theorem, we can say

$\frac{PQ}{AB} = \frac{PM}{AN}$

From (1), we get

$\implies \frac{2}{5} = \frac{PM}{AN}$

$\implies \bold{PM : AN = 2 : 5}$

Thus, the ratio of their corresponding medians is → $\boxed{\underline{\bold{2:5}}}$.

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Also View:

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ∼ ΔPQR prove that AB/PQ = AD/PM

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Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that: (i) ΔABM ≅ ΔPQN (ii) ΔABC ≅ ΔPQR

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