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### Course: High school geometry>Unit 3

Lesson 7: Proofs of general theorems

# Geometry proof problem: squared circle

Sal finds a missing angle using triangle congruence in a diagram that contains sector of a circle inscribed within a square. Created by Sal Khan.

## Want to join the conversation?

• I understood the whole explanation but if I was given the same problem, I wouldn't be able to do it
• that’s so real with me.
• How often will we use proof theorems/problems in real life?
• The math itself may not be too useful, but the critical thinking and logic is.
• He said that the harder geometry problems revolve around drawing the right triangles and visualizing the right lines. How can I get there(Knowing which lines/triangles to draw)?
• In respect to this, a good way to train your brain is just by practicing different types of problems altogether. On KA, a good way to do this is by taking the course challenge multiple times. Of course, you will also need to know the material well enough to use it when it's needed.

You might find it helpful to work on a difficult problem backwards. Say, if you have four lines that intersect at random angles and you need to find one specific measurement that is not offered, you might work backwards from the angle trying to figure out how to get everything you need. You could also work it forwards, finding all the measurements until you know how to get what you need.

But these are the difficulties of math: finding what operations you need to perform and not making small (or large!) mistakes. Anyone else who has tips is welcome to reply, as well. This answer to this question might very well be different to everyone!
• How was it proven that Line EC and Line EB and Line BC are all equal?
• Because ABCD is a square, AB=BC=CD=DA. Because arc AC is part of circle B, that means BE is a radius as well as BA and BC and are, therefore, all equal. When Sal drew EC, he created triangle ECG and showed it was congruent to triangle EBG by SAS. Since BE and EC are both the hypotenuse of congruent triangles, they are equal. So EC=EB=BC.
• So its still considered a triangle if one or more of its legs are not a straight line? As long as it still has three legs that total to 180 degrees?
(1 vote)
• Nope. A triangle must have 3 straight lines with interior angles adding up to 180 degrees.
Happy to help!
• At , How can you just add x+x+30=180 degrees to solve for the missing angles? How would you which one would be 75 degrees?
• They are both 75 because it is an isosceles triangle (two of its sides and two of its interior angles are the same)
• At wouldn't it make sense for the missing angle to be 60˚, because CE could act as a transversal to ∆DEC, so angle CEB = angle DCE. So then the equation would be 2x + 60 = 180. So the two base angles for ∆DEC would be 60˚ right? Wouldn't that be true? Because most of these diagrams aren't draw to scale.
• At he said that angle EDC is x and angle DEC is also x. But how does he know that those two angles equal the same value?