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### Course: Geometry (all content)>Unit 11

Lesson 5: Theorems concerning quadrilateral properties

# Proof: The diagonals of a kite are perpendicular

Sal proves that the diagonals of a kite are perpendicular, by using the SSS and SAS triangle congruence criteria. Created by Sal Khan.

## Want to join the conversation?

• Wouldn't when he talks about the line forming a straight angle, isn't that kind of arbitrary? Since there are two line segments, how can you tell if one isn't slightly off from the other, creating a vastly obtuse 179 degree angle? Would what he had said be equivalent to the protractor postulate?
• Proof 9 holds up because DB was defined as a line segment in the original premise of the question. It's not evident from the diagram, it's evident from the question (identifying AC and DB as line segments).
• At around , is it ok to write "obvious from diagram" in formal proofs?
• At , I would say the reason should be the reflexive property since I was taught that was used in this situation.
• I am a Geometry Honors student and I have lots of difficulty solving proofs. This video was somewhat helpful, but would be even more helpful is somebody cleared this up for me. What exactly is SSS, SAS, ASA, and AAS? I have only learned to state the reasons as definitions, postulates, theorems, and the different properties for solving equations? I would be really grateful if someone can define these four acronyms for me.
• SSS - Side Side Side Postulate (All sides are congruent, therefore the triangles are congruent)

SAS - Side Angle Side Postulate (Two sides with an angle between them are congruent, therefore the triangles are congruent)

ASA - Angle Side Angle Postulate (Two angles with a side in between them on both triangles are congruent, therefore the triangles are congruent)

AAS - Angle Angle Side Theorem (Two angles and a side that is NOT in between them on both triangle are congruent, therefore the triangles are congruent)

Hope that helps. ^_^
• Can you modify the SSS, ASA, SAS, etc. to prove polygons congruent?
e.g. SSSS, ASASA, etc.??
• You could in theory come up with rules like that for polygons with more than three sides. But it would require more congruent pairs than triangles have -- for instance, SSSS wouldn't be enough and not even SASSS. SASAS and ASASA both seem like they would work though. See what you can make of it, you'd be doing the work of real mathematicians!
• I never was good at this.
• Same here, my advice is to rewatch all these congruent videos and take notes it really helps! (Especially in high school, this is going to be a pretty helpful skill)
• i still dont get how to write a proof. my school is teaching me all these weird are hard terms adn this is a lot easier. but i still dont get how to write a proof?
• look at it this way: its just proving the obvious using postulates and theorems. There is no "right way" of writing a proof. As long as you have 3-5 things proving the conjecture and you can prove it no further, you have written your proof correctly.
• The reason for step three and step six should be the reflexive property of congruence, right?
• i learned steps 3 ard 6 as reflexive which means the same thing as shared side.
• bro asked how its perpendicular, just look at it
• it could be 89 or 91 degrees