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# 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. ### saralasMember

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

Let us consider a right angled triangle ABC, right angle at B.
In ABC
A + B + C = 180o (angle sum property of a triangle)
A + 90o + C = 180o
A + C = 90o
Hence, the other two angles have to be acute (i.e. less than 90°).

[In any triangle, the side opposite to the larger (greater) angle is longer]
So, AC is the largest side in ABC.
But AC is the hypotenuse of ABC. Therefore, hypotenuse is the longest side in a right angled triangle.
2. ### saralasMember

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

3. ### saralasMember

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