If ABCD is a parallelogram, then which of the following is true? Options: A . &nbsp AC=BD B . &nbsp AB=AC C . &nbsp ∠ A = 130 ∘ , ∠ C = 130 ∘ , ∠ B = 50 ∘ D . &nbsp A B ⊥ A D

Answer: Option C : C In a parallelogram, the adjacent sides and angles are not equal and no sides are perpendicular to other. ∠ A + ∠ B = 130 ∘ + 50 ∘ = 180 ∘ Here, ∠ A and ∠ B are co-interior angles and their sum is 180 ∘ . By the converse of co-interior angles theorem, AD || BC and AB is the transversal. ∠ D + ∠ A = 50 ∘ + 130 ∘ = 180 ∘ Here, ∠ D and ∠ A are co-interior angles and their sum is 180 ∘ . By the converse of co-interior angles theorem, AB || DC and AD is the transversal.

If ABCD is a parallelogram, then which of the following is true?

Question

If ABCD is a parallelogram, then which of the following is true?

Options:

A . AC=BD

B . AB=AC

C .

∠ A = 130^{\circ}, ∠ C = 130^{\circ}, ∠ B = 50^{\circ}

D .

A B ⊥ A D

Answer: Option C
:
C

In a parallelogram, the adjacent sides and angles are not equal and no sides are perpendicular to other.
$∠ A + ∠ B = 130^{\circ} + 50^{\circ} = 180^{\circ}$
Here, $∠ A$ and $∠ B$ are co-interior angles and their sum is $180^{\circ}$ .
By the converse of co-interior angles theorem, AD || BC and AB is the transversal.
$∠ D + ∠ A = 50^{\circ} + 130^{\circ} = 180^{\circ}$
Here, $∠ D$ and $∠ A$ are co-interior angles and their sum is $180^{\circ}$ .
By the converse of co-interior angles theorem, AB || DC and AD is the transversal.