Question

Prove that the diagonals of a rectangle bisect each other. The midpoint of AC is _____

Answer 1

Answer:

We choose D.

Step-by-step explanation:

Let the midpoint is O

We will use Angle-SIde-Angle principle to prove that the diagonals of a rectangle bisect each other.

Have a look at the two triangles: AOB and DOC, they are congruent because:

• AB = DC
• ∠OAB = ∠DCO because they are alternate angles
• ∠OBA = ∠CDO because they are alternate angles

So we can conclude that: OB = OB  when two triangles: AOB and DOC are congruent.

Similar, apply for the two triangles: AOD and BOC are congruent so we have OA = OC .

=> It proves that the point O simultaneously is the midpoint and intersection point for the diagonals.

=> The midpoint of AC is ($\frac{2a+ 0}{2}$ , $\frac{0 + 2b}{2}$ ) = (a, b), we choose D.

Answer 2

Answer:

(a,b)

Step-by-step explanation:

simply we find the midpoint of AC and the midpoint of Bd by dividing over 2