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In quadrilateral ABCD, diagonals AC and BD bisect one another:


What statement is used to prove that quadrilateral ABCD is a parallelogram?



Angles ABC and BCD are congruent.


Sides AB and BC are congruent.


Triangles BPA and DPC are congruent.


Triangles BCP and CDP are congruent.

In quadrilateral ABCD, diagonals AC and BD bisect one another: What statement is used to prove that quadrilateral ABCD is a parallelogram? Angles ABC and BCD ar class=

Verified Answer :

MissPhiladelphia

From the given statement, you can only directly prove that the segment bisected has congruent parts, by Definition of Bisecting
therefore,  Segment AP is congruent to segment CP. I hope this helps.

boffeemadrid

Answer:

(C) Triangles BPA and DPC are congruent.

Step-by-step explanation:

It is given that In quadrilateral ABCD, diagonals AC and BD bisect one another.

We have to prove that quadrilateral ABCD is a parallelogram.

(A) The given statement is:

Angles ABC and BCD are congruent

The above statement is not correct because these angles forms the corresponding angle pair and thus are not congruent.

Hence, this option is not correct.

(B) The given statement is:

Sides AB and BC are congruent.

The above statement is not correct because the given sides are formed by the same vertex and thus cannot be equal.

Hence, this option is not correct.

(C) The given statement is:

Triangles BPA and DPC are congruent.

The above statement is correct because the given triangles are congruent by the SAS rule of congruency.

Hence, this option is correct.

(D) The given statement is:

Triangles BCP and CDP are congruent.

the above statement is  not correct because the given triangles cannot be congruent using any rule of congruency,

Hence, this option is not correct.