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Chapter 5: Q7 (page 195)

Quad WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.

Given that 鈭�1鈮�鈭�2鈮�鈭�3鈮�鈭�4. Prove that EFGHis a rhombus.

Short Answer

Expert verified

The parallelogram is a rhombus.

Step by step solution

01

Step 1. Check the figure.

Consider the figure.

02

Step 2. Step description.

From the figure, for the lines HE炉and GF炉and the transversal EG炉, the corresponding angles 鈭�1and 鈭�3are congruent.

So, the lines HE炉and GF炉are parallel.

Similarly, for the lines HG炉and EF炉and the transversal EG炉, the corresponding angles 鈭�2and 鈭�4are congruent.

So, the lines HG炉and EF炉are parallel.

Consider the quadrilateral EFGH.

It is known that if pairs of opposite sides of any quadrilateral are parallel, then it is a parallelogram.

03

Step 3. Step description.

Here,HE炉鈭�GF炉 andHG炉鈭�EF炉 so,EFGH is a parallelogram.

Now, for the triangle 鈻�EGF, 鈭�2鈮�鈭�3.

So, the sidesGF炉 andEF炉 are congruent.

As EF炉鈮�GF炉, thus the parallelogramEFGH is a rhombus.

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