A diagonal of a parallelogram bisects one of its angles Show that it is a rhombus...

Name: Lido Learning Solutions
Uploaded: 2022-01-05T06:16:12+00:00
Description: NCERT Exemplar Solutions - Mathematics - class 9 Quadrilaterals Quadrilaterals - Exercise 8.4 solutions written by Lido's expert teachers

Question

A diagonal of a parallelogram bisects one of its angles Show that it is a rhombus

Accepted Answer

Let the parallelogram be ABCD Diagonal AC bisect A CAB CAD Now ABCD and AC is a transversal CAB ACD Again ADBC and AC is a transversal DAC ACB Now A C A C DAC DCA AD CD But AB CD and AD BC Opposite sides of parallelograms AB BC CD AD Thus ABCD is a rhombus

NCERT Exemplar Solutions Class 9 Mathematics Solutions for Quadrilaterals - Exercise 8.4 in Chapter 8 - Quadrilaterals