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andreyandreev [35.5K]
4 years ago
15

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

Mathematics
2 answers:
Aleksandr-060686 [28]4 years ago
7 0

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.

Ulleksa [173]4 years ago
6 0

Answer:

(a,b)

Step-by-step explanation:

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

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