in a parallelogram ABCD the diagonals AC and BD intersect atpoint E . length of AC is 14 and length of BD is 10 what is the length of AE

In a parallelogram, the diagonals bisect each other, meaning that each diagonal is divided into two equal parts at their point of intersection.

Given:
- Length of diagonal \( AC = 14 \)
- Length of diagonal \( BD = 10 \)

Since diagonals bisect each other:
- \( AE = \frac{AC}{2} = \frac{14}{2} = 7 \)

Thus, the length of \( AE \) is **7 units**.

Would you like further details or have any other questions?

Here are some related questions to explore:
1. How do you calculate the length of other segments like \( BE \) or \( EC \)?
2. What are the properties of diagonals in different quadrilaterals?
3. How can we use the diagonals to find the area of a parallelogram?
4. How would this change if the parallelogram were a rectangle or rhombus?
5. How do we prove that diagonals bisect each other in a parallelogram?

**Tip:** In a parallelogram, opposite sides are equal and diagonals bisect each other, which simplifies many calculations!

In a parallelogram ABCD the diagonals AC and BD intersect at point E. The length of AC is 14 and the length of BD is 10. What is the length of AE?

Learn how to calculate the length of AE in a parallelogram where diagonals AC = 14 and BD = 10. This problem explores key geometry concepts such as diagonal bisection in a parallelogram. Ideal for students in Grades 6-8.

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