Point D is placed so that ⬔CBD is a right angle and D is on AC. If necessary, give the answer in simplest radical form. Find the perimeter of the land to the nearest foot.įind the geometric mean of each pair of numbers. Find the area of the land to the nearest square foot. A dirt road makes an altitude to the longest side of the plot and cuts the longest side into two parts that measure 65 feet and 83 feet.Ĩ. He is looking at a plot in the shape of a right triangle.
Greg is interested in buying a plot of land. There are no conditions under which the arithmetic mean will be less than
Name the conditions under which two nonzero, positive numbers, a and b, have an arithmetic mean that is less than their geometric mean. The geometric mean of two positive numbers is the positive square root of their product. Name the conditions under which two nonzero, positive numbers, a and b, have equal geometric and arithmetic means.Ī and b have the same geometric and arithmetic means if a b. The arithmetic mean is also known as the average. The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle.Ĥ. The geometric mean of two positive numbers is the positive of their product. Write a similarity statement comparing the three triangles in each diagram.ġ. Be sure to write the vertices in the correct order. Write a similarity statement comparing the three triangles. The two triangles that are similar to each other and to the original triangle. _1_ and 4 4 įind the geometric mean of each pair of numbers.Īltitude to the hypotenuse of a right triangle forms 2. +įind the geometric mean of each pair of numbers. For Exercises 7–9 complete each similarity ratio comparing the indicated side lengths. The smaller triangles are also shown separated from the big triangle. The big right triangle is divided by an altitude into two smaller right triangles. longer legs and the hypotenuses of the triangles 1 and 2 : shorter legs and the hypotenuses of triangles 1 and 3 : _a xĩ. Find the cross product of your answer to Exercise 7 to prove Theorem 8-1-2.Ĭ _ _ 8. Find the cross products of your answers to Exercises 8 and 9 to prove Theorem 8-1-3.ġ0. Write your answer in simplest radical form, if necessary. Determine what the altimeter would read to the nearest foot when the helicopter is directly above the buoy.ġ2. When the helicopter passes over a buoy that is known to be 1.3 miles from shore, the angle formed by the shore, the helicopter, and the disabled ship is 90. The ship has called in its position as 1.7 miles from shore. The Coast Guard has sent a rescue helicopter to retrieve passengers off a disabled ship. Use the diagram to complete each equation.ġ6. In Exercises 1 and 2, fill in the blanks to complete each theorem or definition. The length of a leg of a right triangle is the geometric mean of the length of the hypotenuse and the segment of the hypotenuse adjacent to that leg.Ī 2 ⫽ xc 2 a ⫽ 4(13) 2 a ⫽ 52 a ⫽ %2 ⫽ 2!3 The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse. You can use geometric means to find side lengths in right triangles. 3 and 27Ĭopyright © by Holt, Rinehart and Winston. 1.įind the geometric mean of each pair of numbers. Write a similarity statement comparing the three triangles in each diagram.
Similarity statement: 䉭ABC 䉭ADB 䉭BDC The geometric mean of two positive numbers is the positive square root of their product. The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle. Similarity in Right Triangles Altitudes and Similar Triangles
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