Question

Crystal is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning coordinates as given.

Answer 1

c,c/2,a+b/2,AE,DE are the answers

Answer 2

Answer:We can fill all the boxes with help of below explanation.

Explanation:

Since here, ABCD is a parallelogram with vertices A, B, C and D and diagonals AC and BD.

Where, it is given A≡(0,0), B≡(a,0) and D≡(b,c)

According to the given figure,

The coordinates of C are (a+b, c) ( since, Both points C and D are equally far from X-axis therefore, they both have same y-coordinate.)

Now, again from the diagram, E is the midpoint of both Diagonals BD and AC.

where, coordinates of E are $(\frac{a+b}{2} ,\frac{c}{2})$

Thus, by the definition of midpoints $AE\cong CE$ and $BE\cong ED$.

Also, BD and AC are intersecting at point E.

Therefore AC and BD bisect each other.