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.

Answer 1

Consecutive angles in a parallelogram should be supplementary. Just by looking at the picture if you add up the values of the angles in each rectangle, you'll see that they are supplementary or be equal to 180°.

Answer 2

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°.