Mathematics, 14.06.2020 03:57 meganxc98

What value of x would make KM ∥ JN? Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.

Complete the statements to solve for x.

By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN.

Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.

Cross-multiply: (x – 5)() = x(x – 3).

Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).

Multiply and simplify: x2 – x – = x2 – 3x.

Solve for x: x = .

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What value of x would make KM ∥ JN? Triangle J L N is cut by line segment K M. Line segment K M goe...