Problem 16 Easy Difficulty

If AD and PM are medians of triangles $\mathrm{ABC}$ and $\mathrm{PQR}$, respectively where
$\Delta \mathrm{ABC}-\Delta \mathrm{PQR}$, prove that $\frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{AD}}{\mathrm{PM}}$.

Answer

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Geometry

NCERT Class 10 - Math

Chapter 6

Triangles

Section 3

Similarity of Triangles

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Problem 15

Problem 16

Video Transcript

We have our number 16 question says if A D and PMR millions, so A D and B. M. Are the millions of the triangle. Well, let us draw the triangles first. Okay. And this is A. B. C. And this is B. You are. So these are the meetings means it will divide this aside busy. It will bisect this busy. Okay, so these are the medians where triangle abc is similar to tangle P Q. R. It has been given. So we have to prove that A B by PQ, A B by BQ will be equal to 80 by the M. So this is A D. And B. M. Okay, so we have been given that these two strangles are similar. So if this is similar, so we can say that angle be equal to angle Q. Yeah. Okay. And A B by peak. You will be called to Bc by you are you know, A B by P Q can Britain as half of B. C. Half of B. C by half of cuba. Because half half get cancelled out now half of B. C. Will be either BD or D. C. So let us write BD over Cuban. Okay no entangle A. BD and pick um Entangled A. B. D. And H. Um These triangles strangle A. B. D. And tangle peak. Um We have already proved A. B. By EQ. Equal to B. D. By. Um that is here and okay so now angle B. Is equal to angle Q. Which is already being approved and will be equal to angle Q. Angle be equal to angle Q. From here. Okay so we can easily see that dangle A BD will be similar to anger PQ. Em by side angle side criteria. So No we can see that maybe by peak you will be equal to 80 by B. M. And improved. Thank you.

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