In a parallelogram opposite sides are equal.
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27
Given,
A parallelogram abcd
To prove,
AB=CD,AD=BC
Construction,
Join AC
Proof,
In triangle ADC and triangle ABC
Angle ACD = Angle CAB(alternate interior angle)
angle CAD=angle ABC(-------||-----)
AC=AC (common side)
by ASA
Triangle ADC congruent triangle ABC
therefore, AB=CD(cpct)
AD=BC (cpct).
A parallelogram abcd
To prove,
AB=CD,AD=BC
Construction,
Join AC
Proof,
In triangle ADC and triangle ABC
Angle ACD = Angle CAB(alternate interior angle)
angle CAD=angle ABC(-------||-----)
AC=AC (common side)
by ASA
Triangle ADC congruent triangle ABC
therefore, AB=CD(cpct)
AD=BC (cpct).
Answered by
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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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