The Angle-Angle-Side (AAS) Theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent. Basically, if you have two triangles and you know two angles and a side that's *not* between those angles are the same, then the triangles are identical!
This is really useful for proving that triangles are the same without needing to know all the side lengths or all the angle measures. It's a shortcut for proving congruence.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Congruent | a. A statement that is accepted as true without proof. |
| 2. Angle | b. Having the exact same size and shape. |
| 3. Side | c. The point where two sides of a polygon meet. |
| 4. Postulate | d. A figure formed by two rays sharing a common endpoint. |
| 5. Vertex | e. A line segment forming part of the outline of a figure. |
Complete the following paragraph about the AAS Theorem:
The AAS Theorem states that if two ______ and a non-______ side of one triangle are ______ to the corresponding two angles and non-included side of another triangle, then the two ______ are ______.
Explain in your own words how the AAS Theorem is different from the ASA (Angle-Side-Angle) Postulate. Give an example to illustrate the difference.
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