Question

Prove that consecutive angles of the parallelogram are supplementary

Answer 1

Step-by-step explanation:

Prove: *If a quadrilateral is aparallelogram, then the consecutive angles are supplementary. Prove:Angle BAD and angle CBA aresupplementary. *This is a proof for a single pair of consecutive angles. To fully prove the statement above, the 3 other pairs of consecutive anglesmust also be proved to besupplementary.

Answer 2

Answer:

AB ∥ CD and AD is a transversal.

We know that interior angles on the same side of a transversal are supplementary.

Therefore, ∠A + ∠D = 180°

Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°.

Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°.

Hence, it is proved that any two adjacent or consecutive angles of a parallelogram are supplementary.

If one angle is a right angle, then all four angles are right angles:

From the above theorem, it can be decided that if one angle of a parallelogram is a right angle (that is equal to 90 degrees), then all four angles are right angles. Hence, it will become a rectangle.

Since, the adjacent sides are supplementary.

For example, ∠A, ∠B are adjacent angles and ∠A = 90°, then:

∠A + ∠B = 180°

90° + ∠B = 180°

∠B = 180° – 90°

∠B = 90°

Similarly, ∠C = ∠D = 90°

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