Question

In ∆ABC, P and Q are the points on AB and AC such that AP = 1.2 cm, PB = 3.6 cm, AQ = 1 cm and QC = 3 cm. Find if PQ is parallel to BC.​

Answer 1

Answer:

By using Thales Theorem, we have [As it’s given that PQ ∥ BC]  A P P B = A Q Q C APPB=AQQC 2.4 P B = 2 3 2.4PB=23  2 x PB = 2.4 x 3  PB = ( 2.4 × 3 ) 2 (2.4×3)2 cm  ⇒ PB = 3.6 cm  Now finding, AB = AP + PB  AB = 2.4 + 3.6  ⇒ AB = 6 cm  Now, considering Δ APQ and Δ ABC  We have,  ∠A = ∠A  ∠APQ = ∠ABC (Corresponding angles are equal, PQ||BC and AB being a transversal)  Thus, Δ APQ and Δ ABC are similar to each other by AA criteria.  Now, we know that  Corresponding parts of similar triangles are propositional.  ⇒ A P A B APAB = P Q B C PQBC  ⇒ PQ = ( A P A B APAB) x BC  = ( 2.4 6 2.46) x 6  = 2.4  ∴ PQ =2.4cm

Answer 2

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By using Thales Theorem, we have [As it’s given that PQ ∥ BC]

• A P/ P B = A Q /Q C
• 2.4 2.4/PB=2/3
• 2 x PB = 2.4 x 3
• PB = ( 2.4 × 3 )/2cm
• ⇒ PB = 3.6 cm
• Now finding, AB = AP + PB AB = 2.4 + 3.6
• ⇒ AB = 6 cm

Now, considering Δ APQ and Δ ABC We have,

∠A = ∠A ∠APQ = ∠ABC (Corresponding angles are equal, PQ||BC and AB being a transversal).

Thus, Δ APQ and Δ ABC are similar to each other by AA criteria.

Now, we know that

Corresponding parts of similar triangles are propositional.

• ⇒ AP/AB = PQ/BC
• ⇒ PQ = (AP/AB) x BC
• = ( 2.4/6) x 6 = 2.4

∴ PQ = 2.4 cm.