Question
Parallelogram Proofs Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
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=
Complete this assessment to review what you’ve learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
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=
Answers
There are no human answers yet.
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 \( 9 \).
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 \( 9 \).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.