Why ssa doesn work

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school. To unlock all 5, videos, start your free trial. Knowing only side-side-angle SSA does not work because the unknown side could be located in two different places. Knowing only angle-angle-angle AAA does not work because it can produce similar but not congruent triangles.

When you're trying to determine if two triangles are congruent, there are 4 shortcuts that will work. Because there are 6 corresponding parts 3 angles and 3 sides, you don't need to know all of them. We said if you know that 3 sides of one triangle are congruent to 3 sides of another triangle, they have to be congruent.

The same is true for side angle side, angle side angle and angle angle side. The reason why these work is because If I give you 3 sides that are congruent there's only one triangle that you can construct, but there's a darker serious side of Geometry that we don't like to talk about and that's the two that don't work. So let's take a look at the first one which is side side angle.

Now part of reason why this is the serial type Geometry is because if you switch around the a you get a square root, but I'm not going to give the gratitude of hearing me say that.

If we start off with this angle, and a side so I'm going to say this is a fixed angle and this is a side that's rigid notice that I drew a ray here and I'm saying that we need to make a triangle here and I'm going to say that this point right here is the center of the circle, so its going to be about a radius of my marker and I'm going to draw in, in dotted lines and again I am not an artist so if we have this circle that is centered at that point, notice that using a radius I can construct two different lines that are congruent so I'm not changing that third side but these two triangles are definitely not congruent.

To redraw them we have this obtuse triangle here so we have these angles as being congruent we have this side being congruent and we have this third side that I haven't marked so we have 1, 2, 3 so we have side side angle and then this other larger triangle that I was able to draw where we have these two angles being congruent cause I kept that fixed, this side was fixed so these two sides must be congruent and this third side because it's a radius of this circle this side must also be congruent but notice we've created two triangles that are not necessarily congruent which is why side side angle is not a shortcut.

The second shortcut that doesn't work is angle angle angle, couple of different ways to look at this one. Is it guaranteed that if Jenna follows the plan, she will create the garden exactly as Felix has envisioned it? There are sometimes two ways to arrange the remaining side and angles!.

Geometry Triangle Congruence Rules. Go to Topic. Explanations 2. Sujay Kazi. The problem is that this yields two solutions for the triangle, and both are equally correct. Thus, we now know that SSA is not a valid congruence rule for a general triangle. However, there are some special cases in which it does work. Related Lessons.

Sequences of Transformations. HL Hypotenuse-Leg Congruence. Sum of Exterior Angles.