Step 1
To solve this problem use coordinate geometry proof.
Use the slope formula. The slope of a line = rise/run to establish that opposite sides are parallel
Step 2
Show all work
 The slope of AB = 4/3
 The slope of CD = (9−5)/(7−4) = 4/3
 The slope of AD = 5/4
 The slope of CB= (9 − 4)/(7− 3) = 5/4
Step 3
Draw a conclusion
 AB  CD and AD  CB because both pairs of opposite sides have the equal slope.
 ABCD is a parallelogram since the opposite sides are parallel

Further Reading
 Euclidean Proof
 Triangle Proof
 isosceles triangle coordinate proof
 images