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in a proof of the pythagorean theorem using similarity, what allows you to state that the triangles are similar in order to write the true proportions c/a=a/f and c/b=b/e ?

a) the geometric mean (altitude) theorem
b) the geometric mean (leg) theorem
c) the right triangle altitude theorem
d) the sss theorem

In a right triangle, if we draw an altitude, from the vertex which contains the right angle, to its opposite side, the triangles at both sides of this altitude are congruent and hence congruent to the whole triangle.

The above is called the Right angle altitude theorem.

In PYthagorean theorem, we use the above theorem to prove the proportionate values are equal.

a. 0.9 Hz b. 0.37 Hz

Step-by-step explanation:

The frequency of the simple pendulum f = (1/2π)√g/l where g = acceleration due to gravity and l = length of pendulum

a. Find the frequency of a pendulum whose length is 1 foot and where the gravitational field is approximately 32 ft/s2

To find f on Earth, g = 32 ft/s² and l = 1 ft

So, f =  (1/2π)√(g/l)

f = (1/2π)√(32 ft/s²/1 ft)

f = (1/2π)√(32/s²)

f = (1/2π)(5.66 Hz)

f = 0.9 Hz

b. The strength of the gravitational field on the moon is about 1/6 as strong as on Earth.. Find the frequency of the same pendulum on the moon.

On the moon when acceleration due to gravity g' = g/6,

f =  (1/2π)√(g'/l)

f =  (1/2π)√(g/6l)

f = (1/2π)√[32 ft/s²/(6 × 1 ft)]

f = (1/2π)√(32/s²)/√6

f = (1/2π)(5.66 Hz)/√6

f = 0.9/√6 Hz

f = 0.37 Hz