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Parallelogram Proofs Practice
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Parallelogram LMNO has two diagonal lines, LN¯¯¯¯¯¯¯¯ and MO¯¯¯¯¯¯¯¯¯ , that intersect at P . The length of LP¯¯¯¯¯¯¯ can be expressed by 3x−4 , and PN¯¯¯¯¯¯¯¯ by the expression x+14 . Identify a pattern regarding the diagonals of the parallelogram to find the value of x.(1 point)
x=

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Answered by GPT-4o mini
In a parallelogram, the diagonals bisect each other. This means that the lengths of segments from the intersection point (P) to the vertices on each diagonal are equal.

In this case, you have:

- \( LP = 3x - 4 \)
- \( PN = x + 14 \)

Since the diagonals bisect each other, we can set the two expressions equal to each other:

\[
3x - 4 = x + 14
\]

Now, solve for \( x \):

1. Subtract \( x \) from both sides:

\[
3x - x - 4 = 14
\]

2. Simplify:

\[
2x - 4 = 14
\]

3. Add 4 to both sides:

\[
2x = 18
\]

4. Divide by 2:

\[
x = 9
\]

So, the value of \( x \) is \( 9 \).

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