Given: Quadrilateral ABCD; AC and BD bisect each other. Prove: That ABCD is a parallelogram

Question

I need help ASAP, link for the geometry problem

Link: https://drive.google.com/file/d/1jeav4gersc74JVun9XFRs3wn-u2h2GNc/view?usp=sharing

Answer 1

Let P be point of intersection of AC and BD.

Two diagonals intersecting form two pairs of vertical angles: <BPA and <CPD; < BPC and <APD.

AP = PC and BP = PB by definition of bisect.

You can prove opposite tringles BPA and CPD are congruent by SAS and opposite sides AB = CD by CPCTE

You can prove opposite triangles BPC and APD are congruent by SAS and opposite sides BC = AD by CPCTE.

Since opposite sides of the quadrilateral are equal, the quadrilateral by definition is a parallelogram.