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### Course: High school geometry>Unit 3

Lesson 6: Theorems concerning quadrilateral properties

# Proof: Rhombus area

Sal proves that we can find the area of a rhombus by taking half the product of the lengths of the diagonals. Created by Sal Khan.

## Want to join the conversation?

• in a rhombus, are the angles alwyas right angles?
• No, a rhombus only means that all the sides are of equal length. A Square, is a Rhombus where all the sides intersect at right angles.
The diagonals of a Rhombus, however, do always intersect at right angles.
• How do you remember the meaning of all the shapes? For example:
- Rhombus
- Kite
- Square
- Rectangle
and so on...
• Try to link the shapes with what you know and your environment. Like, a rhombus looks like someone had sat on a square slightly, the kite would be like a square but tilted forward while a square is taking two 'L's together and putting them on top on each other.
• The plural of rhombus is rhombi, but how does one know which words to say "uses" and which words to say "i"? I've always wondered that.
• Good question. It will depend of which language the word is taken from. Rhombus comes from the greek rhombos. It was then used in latin as rhombus. The plural of a -us word in latin is -i. Sometimes, a foreign word will be anglicized and it will lose its weird (for us) plural form. Language, like mathematics, is conventions that were agreed upon at one point in history and is not always logical. ;)
• But what if it asked a question like "Find the area of rhombus when a side and diagonal are given"
Like when a diagonal is 12 and side is 10 ?
• Since the diagonals of a rhombus are perpendicular, you can use the Pythagorean theorem to find the other diagonal and then find the area.
• whats the difference between perpendicular and parelel?
• For example parallel lines have the same slope and different y intercepts, while a perpendicular line is the negative reciprocal of the other slope.In shapes now parallel lines are basically opposite of each other and don't intersect.While perpendicular lines always for right angles or 90 degree angles.
• If it is already so completely evident that the rhombus is congruent, why must we go through all these steps of trying to prove it? Also, I still don't understand how to use the different congruency methods, like SSS, SAS, ASA, and AAS. Can someone please explain how and when to use each of them?
• This proof that Sal demonstrates is called two-column proof. He is not writing all the steps since he has already given us the steps by word. However, the two-column proof is the basis of proof in geometry, and it is what you use to explain your actions in a problem (as Sal did two videos ago).

The Postulates
Before reading the definitions of these postulates, you should realize that these specific ones are strictly for triangles!

SSS- Side-Side-Side postulate is one method to prove a triangle is congruent to another. You can use this when two triangles have been discovered to share the same three side lengths.

SAS- Side-Angle-Side postulate is another method to prove that one triangle is congruent to another. You can use this when two triangles have been found to share two side lengths. Along with that, one angle that lies between those side lengths is found to have the same measurement as its corresponding counterpart on the other triangle.

ASA- Angle-Side-Angle postulate is the converse of Side-Angle-Side postulate, and is another method you can use to prove two triangles are congruent. ASA is when two angles are found to have shared corresponding counterparts measures on both triangles. Along with that, one side in between those angles is found to have the same length as its corresponding side on the other triangle.

AAS- Angle-Angle-Side postulate is the final method to prove that a triangle is congruent to another. AAS, is very similar to ASA, however it has one key difference. AAS is when you find two angles to be the same measure as their corresponding counterpart on the other triangle. However, in this postulate, the side that is found to be the same length as its corresponding counterpart is not in between the angles; it's next to one of the angles but not the other.

Hope this helps
• Do those brackets Sal uses indicate that you are finding the area? In other words, does writing "[ADC]" mean "the area of ADC".
• Where did you get the 1\4 in the rhombus area video
• Sal says that [ABC] is equivalent to 0.5*AC*0.5*BD and that is equal to 0.25*AC*BD, since 0.5*0.5 is equal to 0.25
• I have a math question on an assignment that is asking this sort of thing, but it calls the shape a parallelogram instead of a rhombus, does the name matter? Could the steps in figuring it out stay the same? Thanks sal...