Similarity in Right Triangles

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Similarity in Right Triangles

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Presentation transcript:

Similarity in Right Triangles 8-1 Similarity in Right Triangles Holt McDougal Geometry Holt Geometry

Warm Up 1. Write a similarity statement comparing the two triangles. Simplify. 2. 3. Solve each equation. 4. 5. 2x2 = 50

The Arithmetic Sequence: This is a sequence where each consecutive number is found by adding or subtracting the previous number by a certain factor. Ex: The Arithmetic Mean: Average the numbers What is the arithmetic mean of 5 and 10?

Find the Geometric Mean between 5 and 25.

In a right triangle, an altitude drawn from the vertex of the right angle to the hypotenuse forms two right triangles.

Write 3 proportions that can be used with this triangle.

Write 3 proportions that can be used with this triangle.

Example 3: Finding Side Lengths in Right Triangles Find x, y, and z.

Find u, v, and w.

To estimate the height of a Douglas fir, Jan positions herself so that her lines of sight to the top and bottom of the tree form a 90º angle. Her eyes are about 1.6 m above the ground, and she is standing 7.8 m from the tree. What is the height of the tree to the nearest meter?

A surveyor positions himself so that his line of sight to the top of a cliff and his line of sight to the bottom form a right angle as shown. What is the height of the cliff to the nearest foot?

Lesson Quiz: Part I Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 8 and 18 2. 6 and 15

3. If PS = 6 and PT = 9, find PR. 4. If TP = 24 and PR = 6, find RS.