SSA Fails, RHS Works
The same arc construction with and without a right angle.
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The second solution is a completely different triangle on the left, but merely the same triangle flipped upside-down on the right.
Look at the measurements given, and decide which rule applies, or that none does.
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How to decide which condition a given set of measurements fits.
Every congruence question in this chapter reduces to one essential habit: list what is equal between the two triangles, and then check WHERE the equal parts sit in relation to each other. Merely counting the number of equal sides or angles is not enough.
A grid sorting cases by how many sides are given and where the angle lies.
The same arc construction with and without a right angle.
The second solution is a completely different triangle on the left, but merely the same triangle flipped upside-down on the right.
Pair five measurement sets from the exercises with their conditions.
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Five mixed cases where the right test must be chosen.
Two engineers check identical triangular frames. They measure all three exterior boundary lengths of one frame and find they exactly match the three exterior lengths of the second frame. Which congruence condition proves the frames are structurally identical?