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ML Aggarwal Solutions Class 10 Mathematics Solutions for Similarity Exercise 13.2 in Chapter 13 - Similarity

Question 8 Similarity Exercise 13.2

A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR?

Give reasons for your answer.

Answer:

Solution:-

Converse to the Basic Proportionality Theorem is if a line splits any two sides of a triangle in the same ratio, then the line must be parallel to the third side.

From the dimensions given in the question,

Consider the ∆PQR

M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Similarity Question 8 Solution image

So, PQ/PA = 12.5/5

= 2.5/1

PR/PB = (PB + BR)/PB

= (4 + 6)/4

= 10/4

= 2.5

By comparing both the results,

2.5 = 2.5

Therefore, PQ/PA = PR/PB

So, AB is parallel to QR.

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