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Chapter 5: Q5 (page 173)

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.

Short Answer

Expert verified

No, the given figure ABCD is not a parallelogram.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

From the given diagram it can be noticed that:

鈭�ABC=鈭�ADC=70掳.

Therefore, 鈭�ABC鈮�鈭�ADC.

That implies the one pair of opposite angles of the quadrilateral are equal.

No information is given about the other pair of opposite angles.

Therefore, the given quadrilateral ABCD is not a parallelogram.

03

Step 3. Write the conclusion.

No, the given figure ABCD is not a parallelogram.

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Most popular questions from this chapter

The pliers shown are made in such a way that the jaws are always parallel. Explain.

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

鈭�ADX鈮�鈭�CBX

Suppose you know that 鈻�SOK鈮�鈻�COA. Explain how you could prove that quadrilateral SACK is a parallelogram.

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:

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

SA炉鈮�KC炉;SK炉鈮�AC炉
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