Mathematics

Given: PQ is a perpendicular bisector of side AB of the triangle ABC.

Prove: Q is equidistant from A and B.

Given: PQ is a perpendicular bisector of side AB of the triangle ABC. Prove: Q is equidistant from A and B. Loci, Concise Mathematics Solutions ICSE Class 10.

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Answer

Join A and Q as shown in the figure below:

Given: PQ is a perpendicular bisector of side AB of the triangle ABC. Prove: Q is equidistant from A and B. Loci, Concise Mathematics Solutions ICSE Class 10.

In ∆AQP and ∆BQP,

⇒ AP = BP [Given]

⇒ ∠QPA = ∠QPB [Each 90°]

⇒ PQ = PQ [Common]

∴ ∆AQP ≅ ∆BQP by SAS axiom.

∴ AQ = BQ [By C.P.C.T.]

Hence, proved that Q is equidistant from A and B.

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