Question

ABCD is a parallelogram.
a.Show that opposite angles of the parallelogram are equal.
b.Compare your answer to part a with a partner's answer. Can you improve his or her answer? Can you improve your own answer?​

Answer 1

Answer:

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.