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0. In a triangle, if the square on one side is equal to the sum of the squares on the other two sides,then prove that the angle opposite to the first side is a right angle.Use the adjoining figure theorem to find the measure of PKR in theadjoining figureTh2 ge63.Answers26 cm |
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Answer» Given: A triangle ABC in which AC² = AB² + BC²To Prove: angleB = 90°. Construction: We construct a APQR right-angled at Q such that PQ= AB and QR = BC Proof: Now, from APQR, we have, PR² = PQ² + QR² [Pythagoras Theorem, as angleQ = 90°] or, PR²= AB²+ BC² [By construction] ...(i) But AC²= AB² + BC 2 [Given] ...(ii) So, AC² = PR² [From (i) and ii AC = PR ...(iii) Now, in triangle ABC and TrianglePQR, AB = PQ [By construction] BC = QR [By construction] AC = PR [Proved in (iii)] hit the like 👍✔️✔️ if you have understood |
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