Mathematics — first biennium · Lesson
Euclid's second theorem links the altitude to the hypotenuse with the two leg projections: h²=p·q.
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: The second theorem uses only the two projections on the hypotenuse. The geometric result is a length, so take the positive square root.
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
The second theorem uses only the two projections on the hypotenuse. The geometric result is a length, so take the positive square root.
Data / situation: In right triangle ABC, AH=16 and HB=9. Find CH.
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