Exercise 35 Page 394

Let's begin by making sense of the two segments individually.

Segment formed by $(a,b)$ and $(c,b)$

It is given that the points $(a,b)$ and $(c,b)$ form a segment. Notice that the $y\text{-}$coordinate of these points is the same. Consequently, this segment is horizontal. The length of a horizontal segment is found by calculating the difference of the $x\text{-}$coordinates of the endpoints.

Segment formed by $(d,e)$ and $(d,f)$

The second segment is between the points $(d,e)$ and $(d,f).$ These two points have the same $x\text{-}$coordinate. Hence, this segment is vertical. The length of a vertical segment is found by calculating the difference of the $y\text{-}$coordinates of the endpoints.

Creating an equation

It is given that the two segments are congruent. This means that they have the same length. Therefore, we know that $L_1=L_2.$ We can write this using the equations created above. Notice that, in this equation, the letters $b$ and $d$ are not used.