Question

03 Show that the opposite angle of parallelogram are
equal.​

Answer 1

Here, ABCD is a parallelogram with AC as its diagonal.

We know, in parallelogram opposites sides are parallel.

So, AB∥DC and AD∥BC

Since, AB∥DC and AC is the transversal

⇒ ∠BAC=∠DCA ---- ( 1 ) [ Alternate angles ]

Similarly, AD∥BC and AC is the transversal.

⇒ ∠DAC=∠BCA ---- ( 2 ) [ Alternate angles ]

Adding ( 1 ) and ( 2 ),

⇒ ∠BAC+∠DAC=∠DCA+∠BCA

⇒ ∠BAD=∠DCB

Similarly, we can prove, ∠ADC=∠ABC

∴ We have proved that, opposite angles of a parallelogram are equal.

solution

Answer 2

Step-by-step explanation:

The opposite angles of a parallelogram are equal (and conversely: if the opposite angles of a quadrilateral are equal, it is a parallelogram) The diagonals of a parallelogram bisect each other (and conversely: if the diagonals of a quadrilateral bisect each other, it is a parallelogram)