Question

(2) In the figure, line l intersects side AC in point P and side BC in point Q such that A-P-C and B-Q-C. If AP = 4, PC = 8, BQ = 3, QC = 6. State with reason whether line PQ is parallel to side AB​

Answer 1

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Answer 2

Line AB is parallel to PQ

GIVEN

ABC is a triangle.

line sigment PQ intersects AC and BC

AP = 4

PC = 8

BQ = 3

QC = 6

TO FIND

Line PQ is parallel to AB

SOLUTION

We can simply solve the above problem as follows -

In ΔABC

AP/PC = 4/8 = 1/2 (equation 1)

BQ/QC = 3/6 = 1/2 (equation 2)

From equation 1 and 2

We can observe that

AP/PC = BQ/QC

According to Proportionality theoram,

If a line is parallel to one side of the triangle, then it divides the two sides of the triangle in equal proportion.

Hence, PQ // AB

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