question_answer

  If a line is drawn parallel to one side of a triangle, the other two sides are divided in the same ratio, prove it. Use this result to prove the following : In the given figure, if ABCD is a trapezium withthen OR State and prove converse of Pythagoras theorem and hence show that in an isosceles triangle ABC with AC = BC and AB2 = 2AC2, prove that

Answer:

    Ist Part         Similarly,                                                        But     (Triangles on same base DE and between same parallells DE, BC) IInd Part                                                              Draw AC, O is intersection of AC and EF. In  and , EO || DC   ?(i) In  and        By (i) and (ii), Hence Proved. OR First Part Book Work Second Part We have, AC = BC and AB2 = 2AC2 Now,        AB2 = 2AC2  AB2 = AC2 + AC2            AB2 = AC2 + BC2                            is a right triangle right-angled at C  [(Given)]