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Corresponding parts of congruent triangles are congruent

When two triangles are congruent, we can know that all of their corresponding sides and angles are congruent too! Created by Sal Khan.

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• Who standardized all the notations involved in geometry?
• Elucid did. There is a video at the beginning of geometry about Elucid as the father of Geometry called "Elucid as the father of Geometry."

Hope that helps!
• How do we know what name should be given to the triangles?
• As far as I am aware, Pira's terminology is incorrect. The three types of triangles are Equilateral for all sides being equal length, Isosceles triangle for two sides being the same length and Scalene triangle for no sides being equal.

Also, depending on the angles in a triangle, there are also obtuse, acute, and right triangle.
• Who created Postulates, Theorems, Formulas, Proofs, etc. and why??
• multiple people, to explain what was the best way to use mathematics.
• what is sss criterion?
• It stands for "side-side-side". If two triangle both have all of their sides equal (that is, if one triangle has side lengths a, b, c, then so does the other triangle), then they must be congruent.
• What does postulate mean?
• A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven.
-Source Internet-
• I need some help understanding whether or not congruence markers are exclusive of other things with a different congruence marker. Is a line with a | marker automatically not congruent with a line with a || marker? Or is it just given that |s and |s are congruent and it doesn't rule out that |s may be congruent to ||s?

Here is an example from a curriculum I am studying a geometry course on that I have programmed. The curriculum says the triangles are not congruent based on the congruency markers, but I don't understand why: https://www.khanacademy.org/computer-programming/a-graph-for-my-schoolwork-again/5793113371787264

FYI, this is not advertising my program. This is the only way I can think of displaying this scenario. I also believe this scenario forces the triangles to be isosceles (the triangles are not to scale, so please take them for the given markers and not the looks or coordinates).

As you can see, the SAS, SSS, and ASA postulates would appear to make them congruent, but the )) and ))) angles switch. Does that just mean ))s are congruent to )))s?

I hope I haven't been to long and/or wordy, thank you to whoever takes the time to read this and/or respond! I will confirm understanding if someone does reply so they know if what they said sinks in for me :)
• I think that when there is a single "|" it is meant to show that the line it's sitting on will only be congruent with another line that has a single "|" dash, when there are two "||" the line is congruent with another "||", etc.
As for your math problem, the only reason I can think of that would explain why the triangles aren't congruent has to do with the lack of measurements. Since there are no measurements for the angles or sides of either triangle, there isn't enough information to solve the problem; you need measurements of at least one side and two angles to solve that problem. Since there are no measurements given in the problem, there is no way to tell whether or not the triangles are congruent, which leads me to believe that was meant to be a trick question in your curriculum.
I hope that helped you at least somewhat :)
(1 vote)
• Are all congruent triangles similar?
• Yes, all congruent triangles are similar. Triangles can be called similar if all 3 angles are the same. This is true in all congruent triangles.
• Trick question about shapes... Would the Pythagorean theorem work on a cube? And if so- how would you do it? would it work on a pyramid... why or why not?
• You can actually modify the the Pythagorean Theorem to get a formula that involves three dimensions, as long as it works with a rectangular prism. Let a, b and c represent the side lengths of that prism. You should have a^2+b^2+c^2=d^2. d would represent the length of the longest diagonal, involving two points that connected by an imaginary line that goes front to back, left to right, and bottom to top at the same time.