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## Geometry (all content)

### Course: Geometry (all content)>Unit 5

Lesson 2: Quadrilateral proofs & angles

# Proof: Rhombus diagonals are perpendicular bisectors

Sal proves that the diagonals of a rhombus are perpendicular, and that they intersect at the midpoints of both. Created by Sal Khan.

## Want to join the conversation?

• What does SSS mean?
• SSS stands for side/side/side and means that all 3 sides of two triangles are congruent and therefore the triangles are congruent.
SAS stands for side/angle/side and means that 2 sides and the angle they form in two triangles are congruent and therefore the triangles are congruent.
There are lots of videos about congruent triangles. here is one about SSS:
• What is the the proof or theorem for all sides of a rhombus being congruent
• There is no proof. It is simply a definition.
That's like asking for a proof of a triangle has 3 sides.
• What helps for finding missing angles for a quadrilateral (this only works if you're good at finding missing angles in triangles) is if, say, one angle is 50, one angle is X, one is 90, and one is 70 (yes, simple numbers). divide the quad in half to get two triangles. Half X, 50, half 90 and half X, 70, half 90. Add 50 and 45 (half 90) and subtract from 180. You get half X (85). Multiply by 2 and there's X. (Just saying, there is probably a simpler way, I sometimes make things a challenge, BUT it works so you can't say there is something wrong with it)
• Actually, your method does not work. It would only work if the shape was a square (or a rhombus), and in your case, it isn't.
The answer your method yields is 170, which is incorrect. The correct answer is 150. Simply add the three known angles together and subtract that from 360, because all the angles in a quadrilateral add up to 360.
The reason your method won't work is because you cannot divide an irregular polygon equally. Take a rectangle for example. If you draw a diagonal from one corner to another, the 90 degree angle is not split in half. One side will equal 30 and the other equals 60.
• what's the difference between a parallelogram and a rhombus, I noticed that sal said that a rhombus has all equal sides but a parallelogram has opposite sides congruent.
• A parallelogram has 2 pairs of parallel sides. A rhombus has 4 sides of equal length. Rhombuses are a sub-category of parallelograms, since all rhombuses have 2 pairs of parallel sides, so all rhombuses are parallelograms, but not all parallelograms are rhombuses. I hope this helps you.
• I'm usually a quick learner, but I don't understand the questions where they give you the statements, I need someone to clarify it a bit. I know how to make my own proofs but I don't understand the ones where they give you a multiple choice. Can someone clarify them a bit for me?
• All sides of a rhombus are equal in length.
• I just wanted to say thank you to Sal for bettering my math education and helping me through educational rough spots
• I get confused because sometimes Sal says to look at the figure, or that something is obvious from the figure. However, there always seems to be the caveat to not trust the drawing.. I'm confused as to when you can use the drawing and when you can't.
• You are correct not to trust the diagram, but we can trust the markings of a diagram such as tick marks or equivalent angles or parallel sides. Sal ends up marking the diagram based on what we know about the rhombus (all sides equal) and what we know about parallelograms (diagonals bisect each other).
• One other point of confusion I have in this proof is when he says that ∠AEB is supplementary to ∠CEB. Why is he able to simply state this? How is it proved that those angles are supplementary?
• Two angles that form a line are by definition supplementary because a line is a straight angle (180 degrees) and the definition of supplementary is two angles that add to be 180 degrees.