Geometric Proofs, SSS, and SAS?

Question

I REALLY need an easy way to figure out problems for geometric proofs. I've tried so hard to understand how to write a proof but it seems IMPOSSIBLE. Are there any tricks I can use to figure out each step?

Also, how do we figure out if a triangle is congruent using SSS, SAS, etc.? Basically, WHAT IS IT and HOW DO YOU USE IT.

Much thanks! Sorry for the caps. I'll gladly choose a best answer.

Answer 1

For solving geometric proofs, you really just have to practice, practice, practice. It's a new way of looking at the world that you have to train your brain to get.

SSS and SAS mean that two triangles are the same if these are the same. Let's say you have a triangle with sides 3, 4, 5 and another triangle with a different orientation with sides 3, 4, 5. These triangles have to be the same.

With a quadrilateral, you can take something with four equal sides and manipulate the angles. A square and a rhombus might have the same side length. Doesn't work with a triangle. It can't flex that way.

Another way is with two sides and the angle between them. If you have a triangle with side 3 and side 4 and the angle between them is 90 degrees, the third side will be 5. No way around it. So any 3-90-4 triangle will be identical to any other 3-90-4 triangle.

ASA is another one. But remember not to make an A-S-S of yourself. A-S-S won't prove equivalency.

Answer 2

SSS = Side Side Side
When all the 3 sides of a triangle are respectively equal to the 3 sides of another triangle, they are congruent by SSS rule.

SAS = Side Angle Side
When 2 sides and the included angle of a triangle are respectively equal to 2 sides and the included angle of another triangle, they are congruent by SAS rule.

Hope this helps.

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Answer 3

Of course SSS stands for side, side, side, if you know the lengths of all three sides of one triangle and they are same for a second triangle then the 2 triangles are congruent by SSS.

SAS stands for side, anlgle (between the two sides), side, if you know these 3 parts of one triangle and they same for a second triangle then the 2 triangles are congruent by SAS.

Study in detail the examples of proofs in your book, 2, 3 or more times if necessary.

A second or even third book would help you because they'll
have or use different examples in showing their proofs.

You need more exposure to more poofs to get the hang of it.

Hope this helps :-)

Answer 4

SSS is when all three corresponding sides are congruent.
SAS is when two corresponding sides are congruent as well as the angle formed by those two sides (the included angle).
AAS is when two corresponding angles are congruent as well as the side opposite the first angle.
ASA is when two angles and their included side (side between the two angles) are congruent.
When you're writing proofs, just think about what postulates or theorems fit and try to use them. See what you can do with the givens. Most of all, practice! The more you do it, the easier it gets.
Good luck!

Answer 5

Well...

If a triangle A has the same length sides as Triangle B, it has to have the same angles... (SSS)

If triangle A has 2 sides and the angle joining them identical to triangle B, the rest of the triangle has to be the same (SAS)

Answer 6

1.D 2. C 3. A 5. A 6

Answer 7

this is a system for proving that 2 triangles are equal.
say there is a triangle ABC and LMN
SSS congruence proves that
side AB=sideLM, BC = MN ,AC=LN all 3 corresponding sides are equal.proves that both triangles are congruent

SAS can be AB = LM and AC=LN and
angle ABC = angle LMN
2 corresponding sides and one set of corresponding angles are equal. proves that both triangles are congruent.

Answer 8

The only way I know to learn proofs is to look at many examples and then attempt writing your own. Unfortunately, this format isn't geometry-friendly; I'd need diagrams to really answer your question.