Question

chloe draws three parallelograms. in each figure, she measures a pair of angles, as shown. what is a reasonable conjecture for chloe to make by recognizing a pattern and using inductive reasoning? in a parallelogram, all angles are congruent in a parallelogram, consecutive angles are congruent. in a parallelogram, consecutive angles are supplementary in a parallelogram, all angles are supplementary

Explanation:

• For the first parallelogram: \(35^{\circ}+ 145^{\circ}=180^{\circ}\)
• For the second parallelogram: \(129^{\circ}+51^{\circ}=180^{\circ}\)
• For the third parallelogram: \(38^{\circ}+142^{\circ}=180^{\circ}\)

Since in each of the three parallelograms Chloe drew, the sum of consecutive angles is \(180^{\circ}\) (they are supplementary), a reasonable conjecture using inductive reasoning (generalizing from specific examples) is that in a parallelogram, consecutive angles are supplementary.

The option “In a parallelogram, all angles are congruent” is wrong because in a parallelogram, opposite angles are congruent (not all angles). The option “In a parallelogram, consecutive angles are congruent” is wrong as shown by the angle - sums above. The option “In a parallelogram, all angles are supplementary” is wrong because supplementary means the sum of two angles is \(180^{\circ}\), and we cannot say all angles (a parallelogram has four angles) are supplementary in the sense of pairwise sums (for example, in a non - rectangle parallelogram, we have two pairs of equal angles, and \(a + b=180^{\circ}\), \(a + a
eq180^{\circ}\) if \(a
eq90^{\circ}\)).

Answer:

In a parallelogram, consecutive angles are supplementary