Question

ABCD
Diagonal AC of a parallelograms
bisects (A show that
it bisects cc also
(is) ABCD is a rhombus​

Answer 1

Answer:

1)Proved below=Show that it bisects ∠C also.

2)Proved below=ABCD is a rhombus

Step-by-step explanation:

Given:-ABCD is a parallelogram in which AC bisects ∠A.

To prove:-1)AC bisects ∠C also

                2)ABCD is a rhombus

Proof:-1)In ΔABC and ΔCDA

                ⇒AB=CD [Given]

                ⇒BC=DA [Given]

                ⇒AC=CA [Commom]

⇒By Side Side Side [S.S.S] congruence rule ΔABC≅CDA

⇒∠3=∠4 [By C.P.C.T][∵C.P.C.T=Corresponding Parts of a Congruent Triangle]

∵AC bisects ∠C also.

2)In a parallelogram opposite angles are equal,

  So,∠A=∠C

⇒1/2∠1=1/2∠3

⇒      ∠1=∠3

In ΔABC

∠1=∠3

AB=BC [∵Equal angles opposite sides are equal]

∴ABCD is a parallelogram

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