EXPLANATION
Given the figure, in order to prove that both triangles are congruent, we can apply the Parallelogram Theorem as shown as follows:
EM ∥ RL ---> 2x+4 = 6x - 8
ER ∥ ML---> x+9 = 4x
The Parallelogram Theorem determine that we have two pairs of congruent sides.
If we have the same value of x in both equations, that means that both pairs are parallel.
Subtracting 2x from 2x+4 = 6x - 8 to both sides:
4 = 6x - 8 -2x
Adding +8 to both sides:
4 + 8 = 6x - 2x
Subtracting and adding like terms:
12 = 4x
Dividing both sides by 4:
12/4 = x
Simplifying:
3 = x
Applying the same procedure for x+9 = 4x give us:
x = 3
Then, bythe SSS Theorem we can assevere that the value of x that will prove the congruency between both triangles is:
x = 3
