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### Course: Integrated math 2>Unit 11

Lesson 9: Proofs with inscribed shapes

# Proof: perpendicular radius bisects chord

Simple proof using right triangle-side-hypotenuse (RSH) congruence criterion to show that a radius perpendicular to a chord bisects it. Created by Sal Khan.

## Want to join the conversation?

• Where can this be used in the real world?
• Computer programming, software, carpentry, and other things
• Is RSH at a real theorem? Or just another name for the HL postulate?
• RSH is actually the HL congruence Theorem
• is the principal root the same as a square root?
• A positive number has two square roots; a negative root and a positive root. The principal square root (that is, the one denoted by the radical sign) is the positive one.
• So a "chord" is just a line, or a line segment or a ray within a circle?...
(1 vote)
• It's a line segment who's ends are on the circumference of the circle.
• I've always wondered this...
At , Sal uses the Pythagorean Theorem, A squared + B squared = C squared
My question is, why can't you just find the square root of both sides of the equation and get rid
of the squared ?
• I understand how am=mc but how does this prove that the radius bisects the chord?
• To "bisect" something means to divide it into two exactly equal parts. Therefore if you "bisect" a line you are cutting it in half giving you two smaller lines of equal measure. Hope that helps.
• Where does the s and the h stand for in this postulate?
• He is calling it RSH, meaning
`R`ight triangle
`S`ide is congruent
`H`ypotenuse is congruent

I have seen it called HL more often, meaning:
`H`ypotenuse is congruent
`L`eg is congruent
• At , what is the principle root of both sides? How can you take the square root of everything? If you can do that, cant Pythagorean theorem be A + B = C? It doesn't seem algebraically correct.
(1 vote)
• The principal root of both sides is the non-negative square root of both sides.
Taking the square root of A^2+B^2 means adding A^2 and B^2 together then taking the square root of the sum. You only get A+B=C if you take the square root of A^2 and B^2 separately then adding it together. If you take A+B=C and square both sides you would get A^2+2AB+B^2=C^2 instead of A^2+B^2=C^2.