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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 5: Q2 (page 182)

The diagonals of $▱ A B C D$ intersecting at Z. For the following figure, tell whether the statement must be, maybe, or cannot be true.
$\bar{D Z} ≅ \bar{B Z}$

Short Answer

Expert verified

The statement must be true.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Apply the concept of the parallelogram.

Diagonals of a parallelogram bisect each other.

03

Step 3. Step description.

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

From the figure, the segments $\bar{D Z}, \bar{B Z}$ are diagonals of a parallelogram.

Since the diagonals of a parallelogram bisect each other therefore the segments are congruent such that $\bar{D Z} ≅ \bar{B Z}$ .

Therefore, $\bar{D Z} ≅ \bar{B Z}$ must be true.

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Most popular questions from this chapter

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

$m ∠ ABC = m ∠ CDA$

Given: ABCDis a $▱, ∠ A ≅ ∠ E$

Prove: localid="1637661691185" $\bar{A B} ≅ \bar{C E}$

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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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