# Geometry 5.7 - PowerPoint PPT Presentation

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Geometry 5.7. The Pythagorean Theorem. Learning Targets. Students will be able to… Use the Pythagorean theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles. Warm-up. Homework Check. Homework Check. Vocabulary. c. a. b. Right Triangles.

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Geometry 5.7

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### Geometry 5.7

The Pythagorean Theorem

### Learning Targets

• Students will be able to…

• Use the Pythagorean theorem and its converse to solve problems.

• Use Pythagorean inequalities to classify triangles.

c

a

b

### Right Triangles

Hypotenuse – Always the longest side.

- Side opposite the right angle.

- Side c is the hypotenuse

Pythagorean Theorem:

c

a

b

Leg – The two shorter sides.

- The sides that make up the right angle.

- a and b are the legs

### Example Type 1: Using the Pythagorean Theorem

Find the value of x

### Example Type 1: Using the Pythagorean Theorem

Find the value of x

### Pythagorean Triples

• Pythagorean Triples – all sides of the right triangle are whole numbers.

• Still use the Pythagorean theorem to find the missing side.

• However, when done if you notice that all three numbers are whole numbers then you have a Pythagorean triple.

• 3, 4, 5 is a Pythagorean triple and any number times 3, 4, and 5 will create a Pythagorean triple.

### Example 2: Identifying Pythagorean Triples

• Find the missing side. Tell if the side lengths form a Pythagorean Triple

### Example 2: Identifying Pythagorean Triples

Find the missing side. Tell if the side lengths form a Pythagorean Triple

### Classifying Triangles

• Tell if the measures can be the side lengths of a triangle. If so classify the triangle.

• Step 1: Determine if a triangle

• Step 2: Classify the triangle

• Classify the triangle using the following chart

### Classifying Triangles

• Tell if the measures can be the side lengths of a triangle. If so classify the triangle.

• A. 8, 11, 13B. 7, 12, 16

### Classifying Triangles

• Tell if the measures can be the side lengths of a triangle. If so classify the triangle.

• C. 5.8, 9.3, 15.6D. 3.8, 4.1, 5.2

### Classifying Triangles

• Tell if the measures can be the side lengths of a triangle. If so classify the triangle.

• E. 5, 7, 10F. 11, 18, 34