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McGraw Hill Integrated II, 2012 View details

1. Geometric Mean

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Exercise 16 Page 623

The given triangle is a right triangle with an altitude to the hypotenuse.

Example Solution: △ QRS ~ △ RTS ~ △ QTR

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We want to write a similarity statement relating the three triangles in the given diagram. To do so we can use the Right Triangle Altitude Theorem.

This theorem tells us about the relationship between the similar right triangles contained in every right triangle that has an altitude to the hypotenuse. Now, let's analyze the given diagram.

As we can see, △ QRS is a right triangle, ∠ QRS is a right angle, and RT is the altitude to the hypotenuse. Having verified the necessary conditions, we can write the similarity statement. △ QRS ~ △ RTS △ QRS ~ △ QTR △ RTS ~ △ QTR Finally, we can combine these three similarity statements into one. Note that there are many possible correct combinations for writing this statement — the triangle names could be written in any order and the names of the triangle could be written in any order. △ QRS ~ △ RTS ~ △ QTR

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Exercises p.623-627

Exercise 16 Page 623

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