Question

EXERCISE 7.4
1. Show that in a right angled triangle, the
hypotenuse is the longest side.
2. In Fig. 7.48, sides AB and AC of A ABC are
extended to points P and Q respectively. Also,
ZPBC<Z QCB. Show that AC >AB.​

Answer 1

Answer:

1. Let ABC be a right angled triangle at B

angle A +angle B +angle C =180°

angle A + 90° +angle C =180 °

angle A+angle C =90°

Hence the other two triangle have to be acute .

angle B is the largest angle in ️ ABC

angle B <angle A

angle B <angle C

AC >BC and AC>AB

We know that in any triangle the side opposite to the larger angle is longer.

AC is the largest side in ️ ABC

AC is the hypotenuse of ️ ABC.

2. In Fig.

angle ABC + angle PBC =180°

angle ABC =180°-angle PBC ..............1

angle ACB +angle QCB =180°

angle ACB =180°-angle QCB....................2

angle PBC < angle QCB

angle ABC> angle ACB

AC > AB .