Mathematics
In the adjoining figure, AP ⊥ l and PR > PQ. Show that AR > AQ.
Triangles
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Answer
Take a point S on PR such that PS = PQ.
Join A and S. Mark angles as shown.
PQ = PS
AP = AP (Common)
∠APQ = ∠APS (Both are equal to 90°)
△APQ ≅ △APS (By SAS axiom)
We know that corresponding parts of congruent triangles are equal.
∠1 = ∠2.
In △ARS,
∠2 > ∠3 (As exterior angle is greater than each interior opposite angle.)
∴ ∠1 > ∠3
⇒ AR > AQ (As side opposite to greater angle is greater.)
Hence, proved that AR > AQ.
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