Therefore, the geometric mean of 12 and 2.4 is
8-1 Geometric Mean
Write a similarity statement identifying the three similar triangles
in the figure.
Find the geometric mean between each pair of numbers.
9. 25 and 16
SOLUTION: By the definition, the geometric mean x of any two numbers a and b is
given by
Therefore, the geometric mean of 25 and 16 is
18. SOLUTION: 10. 20 and 25
SOLUTION: By the definition, the geometric mean x of any two numbers a and b is
given by
Therefore, the geometric mean of 20 and 25 is
11. 36 and 24
SOLUTION: By the definition, the geometric mean x of any two numbers a and b is
given by
Therefore, the geometric mean of 36 and 24 is
By the Geometric Mean (Altitude) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments. The length of this altitude is the geometric mean between the
lengths of these two segments. Solve for x. 12. 12 and 2.4
SOLUTION: By the definition, the geometric mean x of any two numbers a and b is
given by
Therefore, the geometric mean of 12 and 2.4 is
Write a similarity statement identifying the three similar triangles
in the figure.
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By the Geometric Mean (Leg) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments. The length of a leg of this triangle is the geometric mean
between the length of the hypotenuse and the segment of the hypotenuse
adjacent to that leg. Solve for y. Page 1
By the Geometric Mean (Leg) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments. The
length of a leg of this triangle is the geometric mean
8-1 Geometric
Mean
between the length of the hypotenuse and the segment of the hypotenuse
adjacent to that leg. Solve for y. By the Geometric Mean (Leg) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments. The length of a leg of this triangle is the geometric mean
between the length of the hypotenuse and the segment of the hypotenuse
adjacent to that leg. Solve for z. 20. SOLUTION: By the Geometric Mean (Altitude) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments and the length of this altitude is the geometric mean between
the lengths of these two segments. Solve for y . By the Geometric Mean (Leg) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments and the length of a leg of this triangle is the geometric mean
between the length of the hypotenuse and the segment of the hypotenuse
adjacent to that leg. Solve for x. 20. eSolutions
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SOLUTION: Page 2
hypotenuse of a right triangle separates the hypotenuse into two
segments and the length of a leg of this triangle is the geometric mean
between the length of the hypotenuse and the segment of the hypotenuse
adjacent to that leg. 8-1 Geometric
Mean
Solve for x. 49. ERROR ANALYSIS Aiden and Tia are finding the value x in the
triangle shown. Is either of them correct? Explain your reasoning.
By the Geometric Mean (Leg) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments and the length of a leg of this triangle is the geometric mean
between the length of the hypotenuse and the segment of the hypotenuse
adjacent to that leg. SOLUTION: By the Geometric Mean (Altitude) Theorem the altitude drawn to the
hypotenuse of a right triangle separates the hypotenuse into two
segments. The length of this altitude is the geometric mean between the
lengths of these two segments. Solve for z.
Therefore, neither of them are correct.
49. ERROR ANALYSIS Aiden and Tia are finding the value x in the
triangle shown. Is either of them correct? Explain your reasoning.
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