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.

(4, 7)     (8, 9)    

(2, 3)     (6, 5)

Step-by-step 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.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.