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Chapter 5: Q8 (page 168)

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

Short Answer

Expert verified

EFGH is a not parallelogram.

Step by step solution

01

Step 1. Take information from the question

The figure shows a quadrilateral EFGH such that∠HEF=65°and ∠EHG=115°.

02

Step 2. Find the sum of the given angles

Find the sum of the above two angles.

∠HEF+∠EHG=65°+115°=180°

As per Theorem 3.6, if two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

03

Step 3. Check whether EFGH is a parallelogram

For quadrilateral EFGH, HG and EF are cut by transversal HE and same-side interior angles are supplementary.

Therefore,HG∥EF

However, nothing more can be determined about quadrilateral EFGH.

Therefore, quadrilateral EFGH cannot be a parallelogram.

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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.

DX=BX

Find something interesting to prove. Then prove it. Answers may vary.

Given: ▱ABCD;∠1≅∠2

Given: ▱JQKS;PJ¯≅RK¯, Prove: ∠P≅∠R.

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.

For the following figure, if OE=4and WE=8, name two segments congruent to WE¯.
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