To prove:The product of the two legs is equal to the product of the hypotenuse and the length of the altitude drawn to the hypotenuse in a right
Explanation of Solution
Proof:
Consider the following figure.
Here,
ABC is a right-
Also,
If in a right-angled triangle, a perpendicular is drawn from the right angle to the base, the triangles adjoining the perpendicular are similar both to the whole and to each other.
So,
If triangles are similar then the corresponding sides are proportional.
Hence,
So,
In a right triangle, the product of the hypotenuse and the length of the altitude drawn to the hypotenuse equals the product of the two legs
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning