Solve the problem.Show that the midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. [Hint: See the figure below. Show that 
= 
.] 
What will be an ideal response?
Verify that 
= 
.
Cancel the 2's and square both sides:
2 = 
2 or
(a + b)?(a + b) = (a - b)?(a - b) or
a?a + 2a?b + b?b = a?a - 2a?b + b?b [2a?b = 0 since a and b are orthogonal]
a?a + b?b = a?a + b?b Verified.
Thus, the midpoint is equidistant from all three vertices.
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