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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:

∠ABC=∠ADC=70°.

Therefore, ∠ABC≅∠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

Must quad. EFGH be a parallelogram? Can it be a parallelogram? Explain.

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

For the following figure, if WR¯⊥CE¯then name all angles congruent to ∠RCE.

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

∠SKC≅∠CAS;∠KCA≅∠ASK

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 5-7.
See all solutions

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