Mini-Investigation This investigation is in two parts. You will need to complete the

Chapter 11, Problem 16

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Mini-Investigation This investigation is in two parts. You will need to complete the conjecture in part a before moving on to part b. a. The altitude to the hypotenuse has been constructed in each right triangle below. This construction creates two smaller right triangles within each original right triangle. Calculate the measures of the acute angles in each diagram. i. a = , b = , c = ii. a = , b = , c = iii. a = , b = , c = How do the smaller right triangles compare in each diagram? How do they compare to the original right triangle? You should be ready to state a conjecture. Conjecture: The altitude to the hypotenuse of a right triangle divides the triangle into two right triangles that are to each other and to the original b. Complete each proportion for these right triangles. i. ii. iii. Review the proportions you wrote. How are they alike? You should be ready to state a conjecture. Conjecture: The altitude (length h) to the hypotenuse of a right triangle divides the hypotenuse into two segments (lengths p and q), such that . c. Solve for h in the conjecture from part b. The value for h is the geometric mean of p and q. d. Use the Pythagorean Theorem to solve for x and y, then show that these values support the conjecture in part b and the equation in part c.