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### Course: Class 9>Unit 13

Lesson 3: Triangles 7.3

# Geometry proof problem: midpoint

Sal proves that a point is the midpoint of a segment using triangle congruence. Created by Sal Khan.

## Want to join the conversation?

• I am really confused by this entire proof. Can anyone explain it?
• what did he say that AB hade the same segment as CD would that make the statement false?
• No, not necessarily. They are linked with 2 line segments, and they are BOTH line segments, so no, that doesn't automatically declare it false.
Hope this helped.
• Why do you put a tilde "~" over the equal sign when doing proofs? Why do you need to qualify it with "approximately equal to"?
• Firstly ~doesn't mean approximately equal to and secondly if we just use = sign than it just clarify the properties to be same but if we use~sign than it would mean that an object is same to another object in respect of shape size and all,
• Do vertical angles have to be ALWAYS congruent?
• Why did he keep talking about a 'green' color when there was no green?
• I know what you mean, he is talking about a yellow-green. It appears differently on his screen
• When I took Geometry in HS, a looooong time ago, our math instructor provided us with a corollary called CPCFE, Corresponding Parts of Congruent Figures are Equal. Using it, you could conclude that corresponding legs of congruent triangles were equal. Is that old school? I don't see Sal using it anywhere in his lessons.
• I took geometry last year, and used CPCTC ALL the time. It is so useful. Actually, Mr. Khan did use it, he just didn't put it as a step. At , He said that if we know that the triangles are congruent, the corresponding angles are congruent. That is because of CPCTC, or CPCFE, as you called it.
• How do you define transversal? (Spelled it wrong?)
• Transversal: A line that crosses at least two other lines.
• If at , I wanted to prove the remaining angles congruent (m angle BAE = m angle CDE) would I also name them alternate interior angles?

Also, just to be certain, would this be enough to prove the triangles congruent? Thank you.
• At the proof is flawed: SAA is applicable when the angles are on the side. Here angles B and C aren't on equal AE and ED respectfully.
• I see your point. However, I believe there is some confusion between two separate postulates. The postulate used in this video, as Joshua mentioned, is AAS (Angle-Angle-Side). This is a known, valid postulate - the proof and explanation of which is available in earlier videos in this unit.

The postulate which you seem to be alluding to is ASA (Angle-Side-Angle), which is also correct and found earlier in the unit. ASA and AAS are independent from one another. Both valid postulates that we can use to verify the congruency of triangles.

In some cases, if we have the actual angle measures of the angles, we can use the known property about the sum of the angle measures of a triangle to "transfer" from AAS to ASA. AAS already implies that we know two of the angles, which means that we also know the third one. Thus, we can use AAS and ASA interchangeably while still keeping in mind the fact that they are independent postulates that can be used in different scenarios.

Hope this helps!:)
• On the third statement, Sal uses AAS to prove congruency, but would it be possible to use SAS since both of the triangles have a line with a blue arrow?
• There is a distinction to be made between the "tick mark" (>) and the straight "tick" (|) found on lines.

The first symbol (>) tells us that a pair (or higher amount) of lines is parallel. This, of course, does not in any way guarantee that they also have equal length.

The second symbol (|) tells us that a pair of lines has equal length. Inversely, this does not necessarily mean that the two lines are parallel to one another.

So in the diagram shown in the video, we have one pair of parallel lines (denoted by the symbol >) AB and CD. We also have one set of lines with equal length (denoted by the symbol |) AE and ED.

Hope this helps! :)