NCERT Solutions for Class 9th Maths: Chapter 7 Triangles Exercise 7.4

Discussion in 'CBSE Class 9 Maths Help' started by saralas, May 18, 2014.

  1. saralas

    saralas Member

    Show that in a right angled triangle, the hypotenuse is the longest side.

    Answer:

    NCERT Solutions for Class 9th Maths Exercise  7.4 Q1.JPG


    Let us consider a right angled triangle ABC, right angle at B.
    In [​IMG]ABC
    [​IMG]A + [​IMG]B + [​IMG]C = 180o (angle sum property of a triangle)
    [​IMG]A + 90o + [​IMG]C = 180o
    [​IMG]A + [​IMG]C = 90o
    Hence, the other two angles have to be acute (i.e. less than 90°).
    [​IMG]
    [In any triangle, the side opposite to the larger (greater) angle is longer]
    So, AC is the largest side in [​IMG]ABC.
    But AC is the hypotenuse of [​IMG]ABC. Therefore, hypotenuse is the longest side in a right angled triangle.
  2. saralas

    saralas Member

    In the given figure sides AB and AC of [​IMG]ABC are extended to points P and Q respectively. Also, [​IMG]PBC [​IMG][​IMG]QCB. Show that AC > AB.

    NCERT Solutions for Class 9th Maths Exercise  7.4 Q2.JPG
  3. saralas

    saralas Member

    In the given figure,
    [​IMG]ABC + [​IMG]PBC = 180p (linear pair)
    [​IMG][​IMG]ABC = 180o - [​IMG]PBC ... (1)
    Also,
    [​IMG]ACB + [​IMG]QCB = 180o
    [​IMG]ACB = 180o - [​IMG]QCB ... (2)
    As [​IMG]PBC < [​IMG]QCB
    [​IMG] 180° - [​IMG]PBC > 180o - [​IMG]QCB.
    [​IMG][​IMG]ABC > [​IMG]ACB [From equations (1) and (2)]
    [​IMG] AC > AB (side opposite to larger angle is larger)

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