Question

P and Q are the points on the sides AB and AC of a triangle ABC such that AP = 3 cm, AB = 6 cm, AQ = 7 cm and AC = 21 cm. Is PQ||BC? Give reasons for your answer​

Answer 1

Answer:

We have

(Aq__Ac = 3_9 = 1_3

Ap_Ab = 3.5 _10.5 = 1_3

in

Answer 2

Given :- P and Q are the points on the sides AB and AC of a triangle ABC such that AP = 3 cm, AB = 6 cm, AQ = 7 cm and AC = 21 cm.

To Find :- Is PQ || BC .

Solution :-

Let us assume that, PQ || BC .

So, in ∆APQ and ∆ABC we have,

→ ∠APQ = ∠ABC { since PQ || BC ,corresponding angles are equal . }

→ ∠AQP = ∠ACB { since PQ || BC ,corresponding angles are equal . }

then,

→ ∆APQ ~ ∆ABC { By AA similarity. }

therefore,

→ AP/AB = AQ/AC { When two ∆'s are similar, their corresponding sides are in same ratio . }

checking for given values now,

→ 3/6 = 7/21

→ 1/2 ≠ 1/3

therefore, we can conclude that, our assumption of PQ || BC is wrong .

Hence, we can conclude that, PQ is not parallel to BC .

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