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3 years ago

NEED ASAP!!!!

Mathematics

2 answers:

Tatiana [17]3 years ago

8 0

Answer:Triangles BPA and DPC are congruent is used to prove that ABCD is a parallelogram.

Explanation:Here, we have given a quadrilateral ABCD in which diagonals AC and BD bisect each other.

If P is a an intersection point of these diagonals

Then we can say that, AP=PC and BP=PD ( by the property of bisecting)

So, In quadrilateral ABCD,

Let us take two triangles, $\triangle BPA$ and $\triangle DPC$ .

Here, AP=PC

BP=PD,

$\angle APB=\angle DPC$ ( vertically opposite angles.)

So, By SAS postulate, $\triangle BPA\cong \triangle DPC$

Thus AB=CD ( CPCT).

Similarly, we can prove, $\triangle APD\cong \triangle BPC$

Thus, AD=BC (CPCT).

Similarly, we can get the pair of congruent opposite angle for this quadrilateral ABCD.

Therefore, quadrilateral ABCD is a parallelogram.

Note: With help of other options we can not prove quadrilateral ABCD is a parallelogram.

Usimov [2.4K]3 years ago

7 0

Answer: the answer is Triangles BCP and CDP are condruent

Step-by-step explanation:

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