Geometry 5 7
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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

Geometry 5.7

The Pythagorean Theorem


Learning targets

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

Warm-up


Homework check

Homework Check


Homework check1

Homework Check


Vocabulary

Vocabulary

c

a

b


Right triangles

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

Example Type 1: Using the Pythagorean Theorem

Find the value of x


Example type 1 using the pythagorean theorem1

Example Type 1: Using the Pythagorean Theorem

Find the value of x


Pythagorean triples

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

Example 2: Identifying Pythagorean Triples

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


Example 2 identifying pythagorean triples1

Example 2: Identifying Pythagorean Triples

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


Classifying triangles

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 triangles1

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 triangles2

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 triangles3

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


Extra practice 5 7

Extra Practice 5.7


Extra practice 5 71

Extra Practice 5.7


Extra practice 5 72

Extra Practice 5.7


Extra practice 5 73

Extra Practice 5.7


Extra practice 5 74

Extra Practice 5.7


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