Question

Line segments AB and CD bisect each other at O. Let's prove that AC and BD are
parallel. Let's write what kind of quadrilateral is ABCD.​

Answer 1

Step-by-step explanation:

in triangles AOC and DOB

ob=oa(ab and cd bisect each other)

angle dob=angle aoc (vertically opp. angles)

oc=od (ab and cd bisect each other)

triangle AOC is congruent to triangle DOB

by sas criteria

now,

AC=BD (by CPCT)

in quad ABCD

AC=BD

AB and CD bisect each other

so,ABCD is a rectangle