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## High school geometry

### Course: High school geometry>Unit 3

Lesson 6: 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? • At around , is it ok to write "obvious from diagram" in formal proofs? • 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. ^_^
• 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? • 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!
• The reason for step three and step six should be the reflexive property of congruence, right? • Around , Sal says that line segment EB and DE form a straight angle. Is this an assumption, or is there a way to prove this? • How could you reverse this so if you started with only the congruent angles, versus sides? • Shouldn't step one be CD is congruent to CB then step two be CD=CB by the definition of congruence? • Congruence = same shape and same dimension(s)
Here lines CD and CB are equal in dimension-same length, as depicted in the diagram by the two shorter lines that cut both of them)
and shape-both are straight lines (assumed because they are sides of a triangle. One could have been curved but that would not have made a triangle in a flat Euclidean space)
Therefore, they are congruent
Things are congruent BECAUSE they are of the same shape and dimension(s).
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Dimension which is equivalent to magnitude/size is understandable, I found the notion of "shape" bit difficult to grasp. Here's a quote which might help
"In this paper ‘shape’ is used in the vulgar sense, and means what one would normally expect it to mean. [...] We here define ‘shape’ informally as ‘all the geometrical information that remains when location, scale and rotational effects are filtered out from an object.’-Mathematician and Statistician David George Kendall 