Question

Use the following diagram and information to answer the question.
Given: ABCD is a parallelogram. △ABC≅△BCD
Julie wants to prove that ABCD is a square. She uses properties of congruent triangles and parallelograms to prove that ∠A≅∠B≅∠C≅∠D. She must also show that AB≅BC≅CD≅DA to prove ABCD is a square.

What else must Julie do to prove ABCD is a square?
a) Julie can use properties of congruent triangles to show that AB¯≅CD and AD≅BC. Then she can use the definition of parallelogram to show AB≅BC.
b) Julie can use properties of congruent triangles to show that AB≅BC and BC≅CD. Then she can show BC≅AD because opposite sides of a parallelogram are congruent.
c) Julie can use the definition of a parallelogram to show that AB≅BC and BC≅CD. Then she can use the definition of congruent triangles to show BC≅AD.
d)Julie can use properties of congruent triangles to show that AC≅BD. Then she can use the definition of parallelogram to show BC≅AD.

Answer 1

Answer:

  b)  Julie can use properties of congruent triangles to show that AB≅BC and BC≅CD. Then she can show BC≅AD because opposite sides of a parallelogram are congruent

Step-by-step explanation:

On the assumption that Julie must show all four sides to be congruent, the one remaining step after using the properties of congruent triangles is to show that side AD is congruent to the rest of the sides. Answer choice B describes that.

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IMO, Julie is finished after she shows∠A≅∠B and AB≅BC, because a parallelogram will be a square if adjacent sides are congruent (makes it a rhombus) and adjacent angles are congruent (makes it a rectangle). A rhombus that is a rectangle is a square.