Chapter 6.5, Problem 7WE

To determine

Tofill:The blankspace with the signs $<$ , $=$ or $>$ .

Answer to Problem 7WE

The complete statement is $a<b$ .

Explanation of Solution

Given information:

The figure is shown below as:

  

Calculation:

It is known that the sum of complementary anglesis $90°$ . So, the angle opposite to side a is:

  $90°-46°=44°$

Now, consider the two triangles made by the diagonal of the given quadrilateral. Both the triangles are similar as they have a common side, the length of two sides of the triangle is $9$ and the angle of the upper triangle is less than the angle of the lower triangle.

So, by SAS inequality the third side of the upper triangle is less than the third side of lower triangle.

  $a<b$

Therefore, the complete statement is $a<b$ .