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Find the value of x that will prove AMLE ARELM2.: +42 +9ECO4.06.2 - 8R23O 0봉0.5

Find the value of x that will prove AMLE ARELM2.: +42 +9ECO4.06.2 - 8R23O 0봉0.5-example-1
User Banoona
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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

User Jason Carter
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