Question

Using the digits 1 to 9, at most one time each, fill in the boxes so that the points

make a parallelogram. Mathematically, use parallel line or congruent sides to
explain your answer. if there are calculations, include those in your explanation.

Answer 1

(4, 7) (8, 9)

(2, 3) (6, 5)

Explanation:

The definition of a parallelogram is a quadrilateral that has two pairs of opposite equal length parallel sides, including equal opposite angle measurements

To simplify the task, we plot the points on a graph paper for the parallelogram ABCD to get the following points;

B (4, 7) A (8, 9)

C (2, 3) D (6, 5)

The length of the opposite sides AB and CD are;

Length AB = √((9 - 7)² + (8 - 4)²) = √20 = 2·√5

Length CD = √((3 - 5)² + (2 - 6)²) = √20 = 2·√5

The length of the opposite sides AC and BD are;

Length AD = √((9 - 5)² + (8 - 6)²) = √20 = 2·√5

Length BC = √((7 - 3)² + (4 - 2)²) = √20 = 2·√5

The slope of segment AB is (9 - 7)/(8 - 4) = 2/4 =1/2

The slope of segment CD is (5 - 3)/(6 - 2) = 2/4 =1/2

Therefore, since the slopes of segments AB and CD are equal, segments AB and CD are parallel

Similarly, we have;

For segment AD, slope = (9 - 5)/8 - 6) = 4/2 = 2

For segment BC, slope = (7 - 3)/4 - 2) = 4/2 = 2

Therefore, the slopes of segments AD and BC are equal, segments AC and BD are parallel.