State if the following is true or false.

P and Q are points on sides AB and AC respectively of ΔABC, then PQ || BC, where AP= 8 cm, PB = 3 cm, AC = 22 cm and AQ =16 cm.

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True

False

answer is A.

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Detailed Solution

Given figure is,
In the adjacent figure, P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ is parallel to BC and divides the triangle ABC into 2

In the adjacent figure, P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ is parallel to BC and divides the triangle ABC into 2

P and Q are points on sides AB and AC respectively of ΔABC, where AP= 8 cm, PB = 3 cm, AC = 22 cm and AQ =16 cm.
We know,
According to Thales theorem, if a line is drawn parallel to one side of a triangle intersecting the other two sides then it divides the sides in the same ratio.
Apply Thales theorem so as to determine whether the line PQ is parallel to BC. i.e.,

A P P B = A Q Q C

Substitute

8

cm for AP and

3

cm for PB in the fraction,

A P P B = 83

Now, from the figure,

QC = AC - AQ

Substitute 22 cm for AC, and 16 cm for AQ in the fraction

A Q Q C

A Q Q C = 16 22 − 16 ⇒ A Q Q C = 83

As the ratio of the lines AB and AC intersect by the points P and Q is the same that is,

A P P B = A Q Q C

So, the line PQ must be parallel to BC that is PQ || BC.
Thales theorem is valid and hence PQ || BC.
Therefore, the statement is true.
Hence, option 1 is correct.

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