Question

alls,
Diagonal AC of a parallelogram ABCD bisects ANGLE A
(see Fig. 8.19). Show that
(1) it bisects C also,
fii) ABCD is a rhombus.​

Answer 1

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GIVEN :-

ABCD is a Parallelogram.

Diagonal AC Bisect ∠A.

TO FIND :-

i) it bisects C also,

ii) ABCD is a rhombus.

SOLUTION :-

In △ADC & △ABC

AD = BC

∠ADC = ∠ABC

DC = AB

By SAS Congruent Rule,

△ADC ≅ △ABC

So,

∠0CA = ∠BCA

=> ∠C Bisected

Hence,

All the Sides are Equal

=> AB = BC = CD = DA

So,

ABCD is a Rhombus.