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Chapter 5: Q1 (page 182)

The diagonals of ▱ABCD intersecting at Z . For the following figure, tell whether the statement must be, maybe, or cannot be true.

AC¯≅BD¯

Short Answer

Expert verified

The statement cannot be true.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Apply the concept of the parallelogram.

If a parallelogram is a rectangle or square, then diagonals are equal.

03

Step 3. Step description.

Consider ABCD is a parallelogram and diagonals AB and CD intersect at Z.

As the diagonals of a parallelogram are not equal to each other.

If a parallelogram is a rectangle or square, then diagonals are equal but from the figure, it is not equal.

Therefore, AC¯≅BD¯cannot be true.

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Most popular questions from this chapter

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.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD¯≅BC¯

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

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.

Given: ABCDis a ▱,∠A≅∠E

Prove: localid="1637661691185" AB¯≅CE¯
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