Question

Marcus is wanting to prove that parallelogram ABCD is a square. He shows that opposite sides are congruent and opposite sides are parallel. Can he conclude ABCD is a square? Why or why not. Explain your reasoning in complete sentences.

Answer 1

Answer:

It cannot be concluded that ABCD is square.

Step-by-step explanation:

parallelogram is a quadrilateral whose opposite side are parallel

it may or may not have angles right angled.

For a quadrilateral to be square following condition should be satisfied

1: opposite side parallel

2: all side congruent

3: All angles right angle.

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coming back  to question

given

Marcus shows that opposite sides are congruent and opposite sides are parallel.

He says that opposite sides are congruent but no information is given about adjacent side. Adjacent side should also be congruent

Also , criteria of right angle is not also mentioned which is mandatory to prove shape of square.

Based on above information,

ABCD can also be

Rectangle and Rhombus, as both also  have  opposite sides  congruent and opposite sides  parallel.

Hence, it cannot be concluded that ABCD is square.