Question

Given: ABCD

Prove: AC and BD bisect each other at E.

Statements:

Given.
ABCD is a parallelogram.
AB || DC.
∠1 = ∠2; ∠3 = ∠4.
AB = DC.
AE = CE; BE = DE.
ASA (Angle-Side-Angle).
Definition of bisector.
Reasons:
a) Given.
b) Definition of a parallelogram.
c) Given properties of a parallelogram.
d) Corresponding angles are congruent.
e) Opposite sides of a parallelogram are congruent.
f) Definition of a bisector.

Which statement justifies that AC and BD bisect each other at E?

a) Statement 1
b) Statement 5
c) Statement 6
d) Statement 8

Answer 1

Statement 6, based on the definition of a bisector, justifies that diagonals AC and BD bisect each other at E in a parallelogram.

Step-by-step explanation:

The question involves proving that in a parallelogram, the diagonals bisect each other. The correct statement that justifies that AC and BD bisect each other at E is Statement 6, which is derived from the definition of a bisector. This definition states that a bisector divides a segment into two equal parts, hence AE = CE and BE = DE. Since AE and CE are equal, and BE and DE are equal, it follows that AC and BD bisect each other at point E, in accordance with the properties of a parallelogram.