Test for a right angle

Objective. Use the converse of Pythagoras to classify triangles.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Test for a right angle develops a connected mathematical idea rather than an isolated trick. Discover and apply the relationship between right-triangle sides. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Match the side to its role.

1 $Identify the known information, the unknown and any conditions.$
2 $Choose a diagram, table, graph or algebraic representation that exposes the structure.$
3 $Apply the relevant rule one justified step at a time, keeping exact values where useful.$
4 $Check by substitution, inverse reasoning or estimation. The result is hypotenuse | leg.$

Answer: hypotenuse | leg

Concept mastery

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Practice

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Common mistake. A common error in test for a right angle is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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