The following link gives a mathematics lesson that can be used in a congruent triangles lesson. Of all the properties used in congruent triangles SAS needs the most emphasis as the angle must be an included one. This lesson helps the students see what happens when this angle is not an included angle.
I cannot see a better way to teach this concept. I have taught this by drawing two triangles that follow these properties on the board but the lesson was nowhere near as visually stimulating as the geometers sketchpad version. Not only did the students see an example where two triangles followed the SSA property and were not congruent but they were able to change the shape and size of the triangles and see that even though the two triangles were still not congruent the SSA property still stood.
Congruent triangles are a big part of the NSW syllabus and students are required to gain a deep understanding on this topic if they wish to reach or exceed the required outcomes. This lesson will enforce the idea that any two triangles with 2 corresponding sides and an angle can only be proven congruent if the angle is an included angle. This will encourage students to think critically when working with congruent triangles in exams.
This lesson would still need much support from the teacher. For instance two of the sides are equal since they are both the radius of a circle. It can be challenging for students to see this. Some scaffolding is required in the lesson.
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