Similarity in Right Triangles

The relationships and theorems involving similarity in right triangles. Learn about the altitude to the hypotenuse, geometric mean, and corollaries. Practice solving examples to enhance your understanding of the concepts.

• Similar Triangles
• Geometric Mean
• Right Triangle
• Theorems
• Corollaries

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Uploaded on Feb 16, 2025 | 0 Views

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Presentation Transcript

1. 8-4 Similarity in Right Triangles M11.C.1 2.2.11.A OBJECTIVES: 1) TO FIND AND USE RELATIONSHIPS IN SIMILAR RIGHT TRIANGLES.

2. THEOREM The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

3. Vocabulary For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that: ? ?= ? ? **Example: Find the geometric mean of 3 and 12

4. Example Find the geometric mean of 4 and 18.

5. Corollary to Theorem The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse

6. Corollary to Theorem The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.

7. Example: Apply Corollaries 1 and 2 Solve for x and y

8. Example Solve for x and y using the corollaries.