Can you really equate the sides whose lengths are 6x and 2x+1?
Error: The student incorrectly assumed which legs were congruent. Explanation: See solution.
Practice makes perfect
Let's take a look at the steps taken by the student and identify the error. Then, we will find the value of x that makes the triangles congruent.
Error
The student supposed that JK ≅ JM, and concluded that x= 14. If this was true, when substituted into the expressions that represent the length of the other two legs, x= 14 would produce the same value for 4x+4 and 3x-1. Let's see if this is the case.
Side
Expression
x= 1/4
Side Length
KL
4x+4
4( 1/4)+4
5
ML
3x-1
3( 1/4)-1
- 0.25
As we can see, KL ≠ML when x = 14. Therefore, the sides KL and ML are not congruent when x= 14.
Correct the Error
If two triangles are congruent, then they have the same perimeter.
JK+KL+JL=JM+ML+JL
⇕
JK+KL=JM+ML
We can substitute the given expressions into the above equation and solve for x.
