# In the given figure BC = 5 cm, AC = 5.5 cm and AB= 4.6 cm. P and Q are points on AB and AC respectively such that PQ || BC. If PQ = 2.5 cm, find other sides of ΔAPQ.

Given: PQ || BC

To find: AP and AQ

Since, PQ || BC, AB is transversal, then,

APQ = ABC [by corresponding angles]

Since, PQ || BC, AC is transversal, then,

APQ = ABC [by corresponding angles]

In APQ andABC

APQ = ABC

AQP = ACB

APQ ABC [by AAA similarity]

Since, the corresponding sides of similar triangles are proportional

AP = 2.3

Now, taking

AQ = 2.75

Therefore, AP = 2.3cm and AQ = 2.75cm

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