The Pythagorean Theorem and its Converse CHAPTER 8.2.

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Presentation transcript:

The Pythagorean Theorem and its Converse CHAPTER 8.2

Concept

Find Missing Measures Using the Pythagorean Theorem A. Find x.

Find Missing Measures Using the Pythagorean Theorem B. Find x.

A. Find x. A. B. C. D.

B. Find x. A. B. C. D.

Concept

Use a Pythagorean Triple Use a Pythagorean triple to find x. Explain your reasoning.

A.10 B.15 C.18 D.24 Use a Pythagorean triple to find x.

Example 3 A 20-foot ladder is placed against a building to reach a window that is 16 feet above the ground. How many feet away from the building is the bottom of the ladder? A 3 B 4 C 12 D 15 Use the Pythagorean Theorem

Example 3 A.6 ft B.8 ft C.9 ft D.10 ft A 10-foot ladder is placed against a building. The base of the ladder is 6 feet from the building. How high does the ladder reach on the building?

Concept

Example 4 Classify Triangles A. Determine whether 9, 12, and 15 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Example 4 Classify Triangles B. Determine whether 10, 11, and 13 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Example 4 A.yes, acute B.yes, obtuse C.yes, right D.not a triangle A. Determine whether the set of numbers 7, 8, and 14 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Example 4 A.yes, acute B.yes, obtuse C.yes, right D.not a triangle B. Determine whether the set of numbers 14, 18, and 33 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Vectors A vector is represented by a line segment. It has magnitude and direction

Draw a Vector Diagram Suppose Silvio walks twelve blocks West from his house at point A. He then turns and walks five blocks South, ending at point B. Draw a vector diagram to show the path Silvio walked. Draw a vector to show the direct route from point A to B. What is the magnitude of this vector AB?