1) Find the geometric mean of
a) \(2\) and \(18\)
b) \(5\) and \(11\)
c) \(12\) and \(3\)
a) \(2\) and \(18\)
b) \(5\) and \(11\)
c) \(12\) and \(3\)
2) \(\triangle ABC\) is a right triangle with a right angle at \(C\). An altitude is dropped from \(C\) to \(\overline{AB}\). Call the point of intersection point \(D\). Draw the three separate triangles formed, labeling the congruent angles and write a similarity statement for all three triangles. Make sure you have correct correspondence.
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3) From problem #2, why are all three triangles similar?
4) Since they are all similar, then the sides are proportional. Write six proportions based on the sides.
4) Since they are all similar, then the sides are proportional. Write six proportions based on the sides.
12) In a triangle with side lengths \(3\), \(4\) and \(5\) cm respectively, what are the lengths of all three altitudes?
Desmos or GeoGebra Challenge:
Construct a right triangle with an altitude drawn to the hypotenuse.
Solution Bank
Construct a right triangle with an altitude drawn to the hypotenuse.
Solution Bank