Two Triangles, Same SSA
Angle A and side c are fixed. Side a is a circle around B — every point exactly that far away — and the third vertex has to sit where that circle crosses the angle's other ray. Drag a and watch how many crossings that makes.
a = 5.0 — 2 different triangles both fit
The circle crosses the ray twice, in front of A both times.
- Angle A
- 35°
- Side c (AB)
- 7
- Side a (BC)
- 5.0
- Triangles that fit
- 2
Try a length for a
Ready to try some? Triangle congruence worksheets
Where it usually goes wrong
SSS, SAS, ASA and AAS are memorized as a list of shapes that work, with SSA sitting just outside it and no picture of what makes it different. So a student reasonably assumes any two sides and any angle should be enough — three measurements is three measurements — and "SSA doesn't count" reads as an arbitrary exception to keep track of rather than a real construction that visibly breaks.
Try this
- Press "Two triangles". Read all three given measurements off C1's triangle, then off C2's — angle A, side c and side a are identical for both, and the two triangles are still not the same shape.
- Press "Too short". The arc never reaches the dashed ray at all — there is no length AC that could close a triangle with these exact measurements, not zero, not a strange one.
- Press "Long enough", then drag a slightly shorter. Watch a SECOND crossing appear on the ray as the arc grows enough to reach it — the ambiguous zone is not a special case, it is everything between "too short" and "long enough".
Where this goes next
SSA becomes trustworthy again the moment the angle is 90° — the "HL" (hypotenuse-leg) rule for right triangles — because a circle can cross a line perpendicular to it at only one point on either side, which is exactly the tangency case sitting at the boundary of this picture.