prove that in a parallelogram opposite angles are equal
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in a parallelogram opposite angles are equal because in a parallelogram name there is the name parallel, parallel means opposite sides with equal length
and
if the opposite angles in a parallelogram are not equal the angle name will change.
and
if the opposite angles in a parallelogram are not equal the angle name will change.
Vishalk:
please mark as branliest.
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Statement : In a parallelogram, opposite angles are equal.
Given : Parallelogram ABCD
To prove ; ∠A = ∠C and ∠B = ∠D
Proof :
In parallelogram ABCD,
Consider,
AD || BC and AB is transversal
∠A + ∠B = 180° [Co - int. Angles]...... (i)
Now, consider AB || DC and BC transversal
∠B + ∠C = 180° [Co - int. Angles]...... (ii)
From (i) and (ii) we get ;
∠A + ∠B = ∠B + ∠C
∠A = ∠C
∠B = ∠D
Hence, it is proved.
Given : Parallelogram ABCD
To prove ; ∠A = ∠C and ∠B = ∠D
Proof :
In parallelogram ABCD,
Consider,
AD || BC and AB is transversal
∠A + ∠B = 180° [Co - int. Angles]...... (i)
Now, consider AB || DC and BC transversal
∠B + ∠C = 180° [Co - int. Angles]...... (ii)
From (i) and (ii) we get ;
∠A + ∠B = ∠B + ∠C
∠A = ∠C
∠B = ∠D
Hence, it is proved.
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