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## Class 9 (Foundation)

### Course: Class 9 (Foundation)>Unit 10

Lesson 4: Congruence part 1

# 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.

## Want to join the conversation?

• 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 :)
• 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.
• Can someone help me summarize this? I'm really confused right now.
• Definition: Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.

One way to think about triangle congruence is to imagine they are made of cardboard. They are congruent if you can slide them around, rotate them, and flip them over in various ways so they make a pile where they exactly fit over each other.

Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are congruent. Various groups of three will do. Triangles are congruent if:
SSS (side side side)
All three corresponding sides are equal in length.
See Triangle Congruence (side side side).
SAS (side angle side)
A pair of corresponding sides and the included angle are equal.
See Triangle Congruence (side angle side).
ASA (angle side angle)
A pair of corresponding angles and the included side are equal.
See Triangle Congruence (angle side angle).
AAS (angle angle side)
A pair of corresponding angles and a non-included side are equal.
See Triangle Congruence (angle angle side).
HL (hypotenuse leg of a right triangle)
Two right triangles are congruent if the hypotenuse and one leg are equal.
See Triangle Congruence (hypotenuse leg).

Hope this helps!
Calc-Ya-Later!