CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.3 Question 14
14. Sides AB, AC and median AD of a triangle ABC are respectively proportional to sides PQ, PR and median PM of another triangle PQR. Show that
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Solution:
Given:
Construction: In
, extend median AD such that AD = DE. Join B and E and then join C and E.
In
, extend median PM such that PM = MS. Join Q and S and then join R and S.
To Prove:
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Proof: We know that AD = DE by construction and also BD = DC which is given.
Therefore, diagonals of quadrilateral ABEC bisect each other at point D which makes quadrilateral ABEC a parallelogram.
Therefore, AB = CE and BE = AC {Opposite sides of parallelogram are equal} (1)
Similarly, QS = PR and PQ = RS. (2)
We have,
From (1) and (2), we can say that
(3)
From (3), we can say that
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{Triangles are similar if the corresponding sides of triangles are proportional}
Therefore,
{Corresponding angles of similar triangles are equal} (4)
Similarly, we can prove that
(5)
Adding (4) and (5), we can say that
(6)
But, we also have
{Given} (7)
From (6) and (7), we can say that from SAS similarity criterion,
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Hence Proved
Er.Sachchidanand Gupta says
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Jashan says
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Anonymous says
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ayushi says
Thanx it helped me alot
Paras Jain says
Thanks a lot I got 3 bonus marks in tution by doing and understanding from here………:)
pushp says
Thank a lot please upload various theorems like BPT&its converse Pythagoras theorem&, it’s converse, area of similar troangles’ there. It would be a great help to students