# A rhombus is a quadrilateral that has four congruent sides. How would you prove that the diagonals of a rhombus intersect at a point that is the midpoint of each diagonal?

See the proof below

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To prove that the diagonals of a rhombus intersect at a point that is the midpoint of each diagonal, we can use properties of parallelograms.

- Label the vertices of the rhombus as A, B, C, and D.
- Draw the diagonals AC and BD.
- Since a rhombus is a special type of parallelogram, its opposite sides are parallel and congruent.
- Consider triangle ABC. Since AB = BC (due to the definition of a rhombus), and angle ABC = angle BCA (opposite angles of a parallelogram are congruent), triangle ABC is isosceles.
- By the properties of isosceles triangles, the altitude from vertex B will bisect side AC, and similarly, the altitude from vertex C will bisect side AB.
- Therefore, the point of intersection of the diagonals (point E) is equidistant from vertices A and C, and from vertices B and D.
- Hence, point E is the midpoint of both diagonals AC and BD, as required.

Therefore, we have proved that the diagonals of a rhombus intersect at a point that is the midpoint of each diagonal.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Why is a trapezoid a quadrilateral, but a quadrilateral is not always a trapezoid?
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- Two opposite sides of a parallelogram each have a length of #18 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #48 #, how long are the other two sides?
- Can a rhombus be a kite?
- How do you prove that the diagonals of a rhombus are perpendicular?

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