Question

helen draws three parallelograms. in each figure, she measures a pair of angles, as shown. which conjecture is reasonable for helen to make? in a parallelogram, consecutive angles are congruent in a parallelogram, all angles are congruent in a parallelogram, opposite angles are acute in a parallelogram, opposite angles are congruent

Explanation:

• In a parallelogram, consecutive angles are supplementary (sum to \(180^{\circ}\)), not congruent. So the first option is wrong.
• In a parallelogram, angles are not all congruent. For example, in a non - rectangle parallelogram, adjacent angles have different measures. So the second option is wrong.
• In a parallelogram, opposite angles are congruent. They can be acute or obtuse. For example, if one pair of opposite angles is \(39^{\circ}\) (acute), the other pair is \(141^{\circ}\) (obtuse). So the third option is wrong.
• By the property of parallelograms, opposite angles are congruent. In each of the given parallelograms (with angle pairs \(120^{\circ}-120^{\circ}\), \(39^{\circ}-39^{\circ}\), \(80^{\circ}-80^{\circ}\)), the pairs of angles shown are opposite angles.

Answer:

In a parallelogram, opposite angles are congruent.