Rhombus diagonals | Quadrilaterals | Geometry | Khan Academy | Summary and Q&A

TL;DR

The diagonals of a rhombus are perpendicular to each other and bisect each other.

Key Insights

• 🟰 A rhombus is a special type of parallelogram with equal side lengths.
• 🫤 The diagonals of a rhombus are perpendicular to each other, intersecting at a right angle.
• 💦 Dropping an altitude from a vertex of a rhombus creates two symmetric right triangles and bisects the opposite side.
• 🫤 The combination of the altitudes from each vertex forms the diagonals of the rhombus, which are also perpendicular and bisect each other.
• 🫤 The diagonals of any rhombus, as well as any isosceles triangle, are perpendicular to each other and bisect each other.
• ❎ All squares are rhombuses, but not all rhombuses are squares.

Transcript

I want to do a quick argument, or proof, as to why the diagonals of a rhombus are perpendicular. So remember, a rhombus is just a parallelogram where all four sides are equal. In fact, if all four sides are equal, it has to be a parallelogram. And just to make things clear, some rhombuses are squares, but not all of them. Because you could have a r... Read More

Questions & Answers

Q: What is a rhombus and how does it differ from a square?

A rhombus is a parallelogram with four equal sides, while a square is a rhombus with 90-degree angles. All squares are rhombuses, but not all rhombuses are squares.

Q: How are the diagonals of a rhombus related to its sides?

The diagonals of a rhombus are perpendicular to each other and bisect each other. They also intersect at right angles and share the same length as the sides of the rhombus.

Q: What happens when an altitude is dropped from a vertex of a rhombus?

Dropping an altitude from a vertex of a rhombus creates two symmetric right triangles and bisects the opposite side. This altitude is also a median of the triangle formed by the two symmetric right triangles.

Q: Do all isosceles triangles have perpendicular diagonals that bisect each other?

Yes, any isosceles triangle with one side equal to another will have perpendicular diagonals that bisect each other. This is a general property of isosceles triangles.

Summary & Key Takeaways

• A rhombus is a parallelogram with four equal sides.

• Some rhombuses are squares, but not all of them have 90-degree angles.

• The diagonals of a rhombus are perpendicular to each other and bisect each other.