Question

NEED ASAP!!!!

Answer 1

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.

Answer 2

Answer: the answer is Triangles BCP and CDP are condruent

Step-by-step explanation: