SOLUTION: How would you explain the difference between angle-angle-side, angle-side-angle, and side-angle-side to a classmate who thinks the letters look alike?

Question 1107616: How would you explain the difference between angle-angle-side, angle-side-angle, and side-angle-side to a classmate who thinks the letters look alike?
Found 2 solutions by addingup, ikleyn:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
Two triangles are congruent if they have the same size and shape. The four common ways to prove that two triangles are congruent (congruent means exactly equal in size and shape):
.
SSS (side-side-side) = All three corresponding sides are congruent
SAS (side-angle-side) = Two sides and the angle between them are congruent.
ASA (angle-side-angle) Two angles and the side between them are congruent.
AAS (angle-angle-side) = Two angles and a non-included side are congruent.
Each of these has its own postulate to prove that the two triangles are congruent.
.
I hope this helps your friend. Each postulate is too long for me to post here, I'll give you one:
ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. (The included side is the side between the vertices of the two angles).

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
On these postulates (congruence tests for triangles) see the lessons
    - Congruence tests for triangles
    - Problems on congruence tests for triangles
    - Problems on congruence tests for triangles-2
in this site.

Also, you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lessons are the part of this online textbook under the topic "Properties of triangles".

Save the link to this online textbook together with its description

Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

to your archive and use it when it is needed.

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