SAS: two sides and the angle between
Two triangles are drawn separately from the same measurements. Will they match?
The rule
Yes, these two match, because the angle sits between the two sides.
A criterion is a set of measurements that fixes one triangle. Fixing one triangle means every triangle built from those measurements is congruent. SAS is a criterion. It means side, angle, side. The angle must sit between the two sides.
Take sides 7 and 5 with 55° between them. Draw it twice. The two drawings fit exactly on each other.
| Name | Known parts | Fixes one triangle? |
|---|---|---|
| SAS | two sides and the angle between | Yes |
| SSS | three sides | Yes |
| ASA | two angles and the side between | Yes |
| SSA | two sides and an angle not between | Not always |
| AAA | three angles | No |
Three angles give the shape, not the size. A small and a big triangle can share them.
Look at the thick parts. Name the rule they give.
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