Mathematics — first biennium · Lesson
Euclid's first theorem links each leg to the hypotenuse and its projection: the square of the leg equals hypotenuse times projection.
Prerequisites: Similarity and Pythagorean theorem
Goal: Apply both Euclid theorems by linking legs, altitude, hypotenuse and projections.
In this lesson: Apply both Euclid theorems by linking legs, altitude, hypotenuse and projections.
New concept: In a right triangle, the altitude to the hypotenuse divides the hypotenuse into the two projections of the legs. Euclid's theorems connect legs, hypotenuse, projections and altitude; identify these segments before choosing a relation.
How to proceed: Match the leg with the projection beneath it on the hypotenuse. Take the square root only after calculating the product.
You can already assume: Similarity and Pythagorean theorem.
Altitude CH splits hypotenuse AB into projections AH and HB: the three lengths make both Euclid theorems visible.
Completed exercises: 0/5 · Correct on first attempt: 0
Match the leg with the projection beneath it on the hypotenuse. Take the square root only after calculating the product.
Data / situation: In right triangle ABC, AB=50 and AH=32. Find AC.
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Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.