Question

Complete the coordinate proof of the theorem.

Given: ABCD is a parallelogram.

Prove: The diagonals of ​ABCD​ bisect each other.

Parallelogram in quadrant 1 of the coordinate plane with vertices at A begin ordered pair 0 comma 0 end ordered pair, B begin ordered pair a comma 0 end ordered pair, C begin ordered pair a plus c comma b end ordered pair and D.

Enter your answers in the boxes.

The coordinates of parallelogram ABCD are A(0, 0), B(a, 0), C(a+c, b), and D(
,
).

The coordinates of the midpoint of AC¯¯¯¯¯ are ( ​a+c2​,
).

The coordinates of the midpoint of BD¯¯¯¯¯ are (
,​ b2​).

The midpoints of the diagonals have the same coordinates.

Therefore, the diagonals of ​ABCD​ bisect each other.

Answer 1

D(c, b)

Midpoint of AC: ((a + c)/2, b/2)

Midpoint of BD: ((a + c)/2, b/2)

Since the midpoints are the same, the diagonals bisect each other.