8-1 Similarity in Right Triangles - Scott County Schools and 1-30...Holt McDougal Geometry ... Holt...
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Holt McDougal Geometry 8-1 Similarity in Right Triangles Bellringer: 1. Write a similarity statement comparing the two triangles. Simplify. 2. 3. Solve each equation. 4. 5. 2x 2 = 50 ±5
Transcript of 8-1 Similarity in Right Triangles - Scott County Schools and 1-30...Holt McDougal Geometry ... Holt...
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Bellringer:1. Write a similarity statement
comparing the two triangles.
Simplify.
2. 3.
Solve each equation.
4. 5. 2x2 = 50 ±5
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Use geometric mean to find segment lengths in right triangles.
Apply similarity relationships in right triangles to solve problems.
Objectives
Holt McDougal Geometry
8-1 Similarity in Right Triangles
geometric mean
Vocabulary
Holt McDougal Geometry
8-1 Similarity in Right Triangles
In a right triangle, an altitude drawn from the vertex of the right angle to the hypotenuse forms two right triangles.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Example 1: Identifying Similar Right Triangles
Write a similarity statement comparing the three triangles.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Example 1B:
Write a similarity statement comparing the three triangles.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Consider the proportion . In this case, the
means of the proportion are the same number, and
that number is the geometric mean of the extremes.
The geometric mean of two positive numbers is the
positive square root of their product. So the geometric
mean of a and b is the positive number x such
that , or x2 = ab.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Example 2A: Finding Geometric Means
Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
4 and 25
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Check It Out! Example 2a
Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
2 and 8
Let x be the geometric mean.
x2 = (2)(8) = 16 Def. of geometric mean
x = 4 Find the positive square root.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Check It Out! Example 2b
Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
Let x be the geometric mean.
10 and 30
x2 = (10)(30) = 300 Def. of geometric mean
Find the positive square root.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Check It Out! Example 2c
Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
Let x be the geometric mean.
8 and 9
x2 = (8)(9) = 72 Def. of geometric mean
Find the positive square root.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Bellringer:Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form.
1. 8 and 18
2. 6 and 15
Holt McDougal Geometry
8-1 Similarity in Right Triangles
You can use Theorem 8-1-1 to write proportions comparing the side lengths of the triangles formed by the altitude to the hypotenuse of a right triangle.All the relationships in red involve geometric means.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Once you’ve found the unknown side lengths, you can use the Pythagorean Theorem to check your answers.
Helpful Hint
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Example 3: Finding Side Lengths in Right Triangles
Find x, y, and z.
Holt McDougal Geometry
8-1 Similarity in Right Triangles
Check It Out! Example 3
Find u, v, and w.
