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Chapter 5: Q3 (page 195)

Quadrilateral WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.

WX炉鈮�YZ炉,XY炉鈮�ZW炉anddiag.WY炉鈮�diag.XZ炉

Short Answer

Expert verified

The quadrilateral is a rectangle.

Step by step solution

01

Step 1. Apply the following concept.

If both pairs of opposite sides of a quadrilateral are equal, then it's a parallelogram.

The diagonals of a rectangle are congruent.

02

Step 2. Step description.

Consider that WX炉鈮�YZ炉,WX炉||YZ炉.

That is, both pairs of opposite sides of the quadrilateral are congruent.

Since one pair of the quadrilateral is parallel and congruent, therefore the quadrilateral is a parallelogram.

03

Step 3. Step description.

Also diag.WY炉鈮�diag.XZ炉.

Since the diagonals are congruent, thus the parallelogram is a rectangle.

Therefore, the parallelogram is a rectangle.

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Most popular questions from this chapter

Prove: If a segment whose endpoints lie on opposite sides of a parallelogram passes though the midpoint of a diagonal, that segment is bisected by the diagonal.

Give the reason for each step in the following proof of theorem 5-6

Given: m鈭�A=m鈭�C=x;m鈭�B=m鈭�D=y

Prove: ABCD is a parallelogram.

Proof:

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-5.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.
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