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
By signing up, you agree to our Terms of Service and Privacy Policy
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.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
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?
- A parallelogram has sides with lengths of #14 # and #12 #. If the parallelogram's area is #84 #, what is the length of its longest diagonal?
- 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?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7