InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
prove pythagorous |
|
Answer» Pythagoras TheoremStatement: In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.Given: A right triangle ABC right angled at B.To prove: AC2\xa0= AB2\xa0+ BC2Construction: Draw BDACProof :We know that: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.ADBABCSo,(Sides are proportional)Or, AD.AC = AB2\xa0... (1)Also,BDCABCSo,Or, CD. AC = BC2\xa0... (2)Adding (1) and (2),AD. AC + CD. AC = AB2\xa0+ BC2AC (AD + CD) = AB2\xa0+ BC2AC.AC = AB2\xa0+ BC2AC2\xa0= AB2\xa0+ BC2Hence Proved. See textbook |
|