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Math / Geometry / Grade 9 / mg9t1

Name Right-Triangle Sides

Find the right angle first, then identify side roles for a chosen acute angle.

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The hypotenuse lies across from the right angle. For the chosen acute angle, the opposite side does not touch that corner. The adjacent leg touches that corner but is not the hypotenuse. The two legs exchange roles when you choose the other acute angle. Use the letters and stated lengths, not the orientation or size of the schematic drawing.

Worked example

In triangle ABC, C is the right angle, AC = 12, BC = 5 and AB = 13. For angle A, AB is the hypotenuse, BC is opposite and AC is the adjacent leg. For B, the legs exchange roles but AB remains the hypotenuse.

Triangle DEF has a right angle at E, DE 9 units, EF 12 units and DF 15 units. Angle D is marked. The drawing is schematic.
Use DEF for all five questions. When a question changes the chosen angle, keep the same triangle.
Question 1 Triangle DEF is right angled at E. Which side is its hypotenuse?
Question 2 For angle D, which side is opposite?
Question 3 For angle D, which side is the adjacent leg?
Question 4 Now choose angle F. Which side becomes opposite?
Question 5 A student says DF is the adjacent leg to D because it touches D. What is the correction?