In with right angle at

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

In △ABC\triangle ABC with right angle at BB, a student attempted to prove that AC2=AB2+BC2AC^{2} = AB^{2} + BC^{2}. The following statements were recorded but are jumbled and missing reasons. P: ∠ADB=∠CBA\angle ADB = \angle CBA Q: △ADB∼△ABC\triangle ADB \sim \triangle ABC R: AB2=AD⋅ACAB^{2} = AD \cdot AC S: AD+DC=ACAD + DC = AC T: AC2=AB2+BC2AC^{2} = AB^{2} + BC^{2} U: DC⋅AC=BC2DC \cdot AC = BC^{2} V: △BDC∼△ABC\triangle BDC \sim \triangle ABC (i) Arrange the statements in a logical order suitable for a complete proof. (ii) For each similarity statement you list, write the specific pair of equal angles that justifies the similarity. (iii) Using the ordered statements and appropriate reasons, complete the proof that AC2=AB2+BC2AC^{2} = AB^{2} + BC^{2}.

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