Answer:
Step-by-step explanation:
Let ABCD be the parallogram.
A,B,C and D are vertices in that order.
Since ABCD is a parallelogram, we get opposite sides are parallel
AB || CD
AD is a transversal making interior angles as A and D
By parallel lines properties we have A +D =180...i
Similarly since BC||AD, and AB is a transversal
Angle A+B =180...ii
We have from i and ii, Angle B = angle D
On the same grounds, as above, we can prove that
Angle A = Angle C
It follows that in a parallelogram opposite angles are equal.
Answer:
We have given a parallelogram ABCD
By the property of parallelogram [tex]AB\parallel CD[/tex]
And [tex]BC\parallel AD[/tex]
Prove: m∠A=m∠C
And m∠B=m∠D
If we join the diagonal AC we will get ΔABC and ΔADC
By alternative interior angles theorem ∠CAB =∠ACD
And by the same theorem ∠DAC=∠ACB
AC=AC(Reflexive)
By ASA Congruency the ΔABC≅ΔADC
By CPCTC m∠B=m∠D
Similarly, If we join diagonal BD we will get ΔABD≅ΔCBD
BY CPCTC m∠A=m∠C
Hence, Opposite angles of a parallelogram are congruent.
