How can you create an equation knowing that the segments are congruent?
Equation: |a-c|=|e-f| Letters not used: b and d
Practice makes perfect
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-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-coordinates of the endpoints.
L_1=| a- c|
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-coordinate. Hence, this segment is vertical. The length of a vertical segment is found by calculating the difference of the y-coordinates of the endpoints.
L_2=| e- f|
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.
L_1=L_2 ⇒ |a-c|=|e-f|
Notice that, in this equation, the letters b and d are not used.
