NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.4 – Part 2

Side opposite angle

Give the side opposite angle made triangle of ABC ,the figure give information of all point's opposite side.

Give the Side Opposite Angle

Give the side opposite angle made triangle of ABC ,the figure give information of all point's opposite side.

3. In the figure, B<A and C<D . Show that AD<BC .

 Give two join triangle AOB and DOC , ∠B < ∠A and ∠C < ∠D and AD>BC

Give Two Join Triangle AOB and DOC

Give two join triangle AOB and DOC , ∠B < ∠A and ∠C < ∠D and AD>BC

Solution:

Given, B<A and C<D

  • Now,

    AO<BO …………..equation(1) (Side opposite to the smaller angle is smaller) OD<OC ……………..equation(2) (Side opposite to the smaller angle is smaller)

  • Adding (1) and (2) AO+OD<BO+OCAD<BC

Q-4 AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Figure)Show that A>C and B>D.

Give quadrilateral ABCD that AB and CD are respectively the smallest and longest sides

Give Quadrilateral ABCD

Give quadrilateral ABCD that AB and CD are respectively the smallest and longest sides

Give, AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD

  • In ΔABD, AB<AD<BD (see the figure) ADB<ABD …………….equation(1) (Angle opposite to longer side is larger.)

  • Now,In ΔBCD , BC<DC<BD (see figure) BDC<CBD ……………….equation(2) (Angle opposite to longer side is larger.)

  • Adding (1) and (2) we get, ADB+BDC<ABD+CBD ADC<ABCB>D

  • Similarly, In ΔABC , ACB<BAC ……….equation(3) (Angle opposite to longer side is larger.)

  • Now,In ΔADC , DCA<DAC …………….equation(4) (Angle opposite to longer side is larger.)

  • Adding (3) and (4) we get, ACB+DCA<BAC+DACBCD<BADA>C

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