If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Δ ABC, AP = 2.4 cm, AQ = 2 cm, QC = 3 cm, and BC = 6 cm. Also, PQ ∥ BC. Required to find: AB and PQ. 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 = 2.4 cm.Read more on Sarthaks.com - https://www.sarthaks.com/634322/in-abc-and-are-the-points-sides-ab-and-ac-respectively-such-that-pq-bc-if-ap-cm-aq-cm-qc-cm-and-bc
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Step-by-step explanation:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
Hence
QC
AQ
=
PB
AP
3
2
=
PB
2.4
PB=3.6cm
AB=AP+PB=2.4+3.6=6cm
As PQ∥BC
∠AQP=∠ACB
∠APQ=∠ABC
So by AAA △AQP∼△ACB
Hence
AC
AQ
=
CB
QP
5
2
=
6
QP
QP=2.4cm
So AB=6cm and QP=2.4cm
Answer:
Δ ABC, AP = 2.4 cm, AQ = 2 cm, QC = 3 cm, and BC = 6 cm. Also, PQ ∥ BC. Required to find: AB and PQ. 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 = 2.4 cm.Read more on Sarthaks.com - https://www.sarthaks.com/634322/in-abc-and-are-the-points-sides-ab-and-ac-respectively-such-that-pq-bc-if-ap-cm-aq-cm-qc-cm-and-bc