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.

Solution-

1st statement- In a parallelogram, all angles are congruent.

If all the angels are congruent then all angles will be 90° (as summation of all the angles are 360° and 360/4= 90°), then it will be either a rectangle or a square, not a parallelogram.

2nd statement- In a parallelogram, consecutive angles are congruent.

If consecutive angles are congruent, then it will be rectangle or a square, not a parallelogram. In a parallelogram, opposite angles are congruent not consecutive angles.

4th statement- In a parallelogram, all angles are supplementary.

In a parallelogram, all the consecutive angles are supplementary or summation of measurements consecutive angles is 180°, not all the angels are supplementary, because opposite angles can't be supplementary.

3rd statement- In a parallelogram, consecutive angles are supplementary.

This is the reasonable conjecture for a parallelogram, because always the summation of measurement of consecutive angles are 180°.

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