8.1 Geometric Mean Objective: Find the geometric mean between two numbers, and solve problems involving right triangle and altitude relationships.

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Presentation transcript:

8.1 Geometric Mean Objective: Find the geometric mean between two numbers, and solve problems involving right triangle and altitude relationships.

Find the geometric mean between 3 and 12. Let x represent the geometric mean. Find the geometric mean between 3 and 12.

Separate the triangles into two triangles along the altitude. Write a similarity statement identifying the three similar triangles in the figure. Then sketch the three triangles, reorienting the smaller ones so that their corresponding angles and sides are in the same position as the original triangle.

Write a similarity statement identifying the three similar triangles in the figure. A. ΔLNM ~ ΔMLO ~ ΔNMO B. ΔNML ~ ΔLOM ~ ΔMNO C. ΔLMN ~ ΔLOM ~ ΔMON D. ΔLMN ~ ΔLMO ~ ΔMNO A B C D

Find c, d, and e.

Find e to the nearest tenth. B. 24 C. 17.9 D. 11.3 A B C D

Find XZ given XY is an altitude.

KITES Ms. Alspach is constructing a kite for her son KITES Ms. Alspach is constructing a kite for her son. She has to arrange two support rods so that they are perpendicular. The shorter rod is 27 inches long. If she has to place the short rod 7.25 inches from one end of the long rod in order to form two right triangles with the kite fabric, what is the length of the long rod?