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Chapter 5: Q3 (page 182)

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

AD¯∥BC¯

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.

A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

03

Step 3. Step description.

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

The segments AD¯,BC¯are the diagonals of a parallelogram.

Since a quadrilateral is a parallelogram if both pairs of opposite sides are congruent thus AD¯∥BC¯.

Therefore, AD¯∥BC¯must be true.

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Most popular questions from this chapter

For the following figure, if WR¯⊥CE¯then name all segments congruent to WE¯.

You can use a sheet of lined notebook paper to divide a segment into a number of congruent parts. Here a piece of cardboard with edge AB¯is placed so that AB¯is separated into five congruent parts. Explain why it works.

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

Given: m∠A=m∠C=x;m∠B=m∠D=y

Prove: ABCD is a parallelogram.

Proof:

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

SA¯≅KC¯;SA¯∥KC¯

Prove Theorem 5-3.
See all solutions

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