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Chapter 5: Q34 (page 171)

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

Given: 鈻�EFIH;鈻�EGHJ;鈭�1鈮�鈭�2

Short Answer

Expert verified

It is proved that 鈭�EGF鈮�鈭�HJI.

Step by step solution

01

Step 1. Description of step.

The opposite sides of a parallelogram are congruent.

In 鈻�EFIH, EF炉and HI炉are the opposite sides of a parallelogram therefore, EF炉鈮�HI炉.

In 鈻�EGHJ, EG炉and HJ炉are the opposite sides of a parallelogram therefore,EG炉鈮�HJ炉.

02

Step 2. Description of step.

Consider 螖EGFand 螖HJIin which EF炉鈮�HI炉,EG炉鈮�HJ炉 and鈭�1鈮�鈭�2 then by SAS postulate 螖EGF鈮�螖HJI.

03

Step 3. Description of step.

As 螖EGF鈮�螖HJI, then by corresponding parts of congruent triangles, 鈭�EGF鈮�鈭�HJI.

Therefore, it is proved that 鈭�EGF鈮�鈭�HJI.

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Most popular questions from this chapter

The coordinates of the three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.

(3,4),(9,4),(6,8)

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

AD炉鈭�BC炉

Prove Theorem 5-1.

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

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.
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