Rather, it only focuses only on corresponding, congruent sides of triangles in order to determine that two triangles are congruent. A pair of congruent triangles is shown below. Can we make restrictions such that SAA is true on a sphere? This suggestion stems from our desire to see what is common between the plane and the other two surfaces, as much as possible.

Starting SAA. Make sure you see what it is in your argument that doesn't work for large triangles. ECD are congruent, we will be able to prove that the triangles are congruent because we will have two corresponding sides that are congruent, as well as congruent included angles.

Let us try it as an initial step in our proof of SAA. Suggestions Start investigating SSS by making two triangles coincide as much as possible, and see what happens.

What about on a hyperbolic plane? Try each counterexample on the plane, on a sphere, and on a hyperbolic plane and see what happens. Counterexample to RLH on a sphere.

Let's consider our triangle ABC and let's copy two of the angles and a non-included side.

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Understanding Congruent Triangles in Geometry