The right triangle altitude theorem - practice problems - page 3 of 4

Euclid was a Greek mathematician and philosopher. He left us with two important but simple theorems that apply in a right triangle.

Euclid's first theorem (about height): The area of the square constructed above the height of the right triangle (h) is equal to the area of the rectangle constructed from both sections of the hypotenuse (c1 and c2):
h2=c1c2

Or: The height in a right triangle is the geometric mean of two sections of the hypotenuse.
h=c1c2

Euclid's second theorem - about the hypotenuse: The area of the square constructed above the hypotenuse of a right-angled triangle is equal to the area of the rectangle constructed from the hypotenuse and the segment of the hypotenuse adjacent to this hypotenuse.

a2=cc1
b2=cc2

Or: The hypotenuse of a right triangle is the geometric diameter of the hypotenuse and the adjacent section of the hypotenuse.

a=cc1

It is usually taught in high school. The Pythagorean theorem can be easily proved using Euclid's theorems.

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 63


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