Question

diagonal AC of a parallelogram ABCD bisects angle A . Show that


1. it bisects angle C also

2. ABCD is a rhombus


Answer with figure plz it's urgent
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Answer 1

Solution

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T.P (i) AC bisects C

i.e., ∠3=∠4

(ii) ABCD is rhombus

Sol:

∠1=∠2

∠2=∠3 (alternate opposite)

∠1=∠4

i.e., ∠ACD=∠CAD

AD=CD (opposite sides of equal angle in a triangle are equal)

but AB−CD and AD=BC

⇒AB=BC=CD=DA

Thus ABCD is a rhombus

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