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Jada and Tyler were playing the Info Gap, using this triangle.
Tyler asked, “Can I have 2 sides and an angle?”
Jada told Tyler that one angle was , one side was 5 cm, and one side was 4 cm. Here is the triangle Tyler made:
If we know that every pair of corresponding parts is congruent, then we know the two triangles are congruent. But we don’t need that much information. If we know the angles of a triangle are 30 degrees and 60 degrees, we can figure out that the third angle is 90 degrees. So when we start drawing a triangle, the triangle is complete before we measure every angle. Figuring out which sets of measurements are enough to draw a complete triangle tells us which sets of measurements are enough to prove triangles are congruent. Here are 3 sets of measurements that appear to be enough information to prove that the two triangles will be congruent: