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Chapter 5: Q7 (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. Properties of a parallelogram

It is known that a parallelogram is a quadrilateral whose both pairs of opposite sides are parallel.

02

Step 2. Check the pair of equal angles

It can be observed from the above figure that the opposite angles ∠HEFand ∠HGFare not congruent.

03

Step 3. Check whether EFGH is a parallelogram

As discussed above that, the pair of the opposite angles are not equal.

So by theorem 5-2 which states that the relationship between two angles that are related to a parallelogram and positioned on the opposite side of each other is congruent, it can be said that EFGH is not a parallelogram.

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