AAS: two angles and any side
Show on a big screenTwo angles are given. The side is not between them. Is that enough?
- Angles 70° and 60° are given. A side of 8 is next to the 60°, not between the two.
- The third angle is filled in: 180° − 70° − 60° = 50°.
- The side of 8 now sits between the 60° and 50° corners.
The rule
Yes, if the two angles total under 180°: they give the third.
A triangle's three angles total 180°. So two angles give the third one.
Now the third angle is known. The side of 8 sits between the 60° and 50° corners. That is ASA, and ASA fixes one triangle.
AAS means two angles and a side that is not between them. If two angles total under 180°, AAS fixes one triangle.
A second example has angles 65° and 48°. They total 65 + 48 = 113°. The third angle is 180 − 113 = 67°. Let a side of 9 join the 48° and 67° corners. It sits between two known angles. That is ASA, so one triangle fits.
Slide the second angle. Watch the third angle change.
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Try the lab to finish this lesson.