Two corners and a side
Two corners and a length. Is that enough for a triangle?
Slide the first angle. Draw it from both ends.
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- The base: 70 mm.
- A 50° ray from the left end.
- A 75° ray from the right end.
- The rays cross once. That is the third corner.
Two corners and a side
Yes, if the two corners add to less than 180°. One triangle fits.
ASA: two angles and the side between them give one triangle. A is an angle and S is a side.
The third angle needs no measuring. The three corners add to 180°. So 50° and 75° leave 180 − 50 − 75 = 55°.
AAS: two angles and a side that is not between them. The side must sit in the same place in both triangles. Find the third angle first. Then the side is between two known angles. So ASA applies.
Example: corners 45° and 65°. A 5 cm side is across from the 45° corner. The third corner is 180 − 45 − 65 = 70°. The 5 cm side now lies between the 65° and 70° corners. So ASA applies.