Lesson 2 Pythagorean Theorem

Last updated 4 months ago

30 Nsɛmmisa

Review of Right Triangle (Geometric Mean) Proportions

Exploration of the Pythagorean Theorem

NOTES on the Pythagorean Theorem

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Use the Pyhthagorean Theorem to Find the Hypotenuse when given both legs

Use the Pyhthagorean Theorem to Find A Leg when given the Hypotenuse and the other Leg

More Practice

Pythagorean Triples

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Find missing leg or hypotenuse of a NON-Pythagorean Triple (not mickey mouse side length)

More and more Practice Finding a missing side of a right triangle Using the Pythagorean Theorem

Converse of the Pythagorean Theorem

Lesson 2 Pythagorean Theorem

Last updated 4 months ago

30 Nsɛmmisa

Review of Right Triangle (Geometric Mean) Proportions

Write in simplest radical form.

Write in decimal form.

Exploration of the Pythagorean Theorem

What do you notice about this image?

What do you wonder about this image?

Determine the area of each square.

Lengths

Blue Area

Green Area

Blue +Green Area

Red Area

3-4-5

5-12-13

6-8-10

Based off of the data in the table from the previous slide, what relationship seems to be true?

Using the dynamic applet on the following slide, does the relationship you noticed appear to be true for any right triangle? Is it true for any triangle? Use numbers from the diagram to justify your answer

NOTES on the Pythagorean Theorem

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Label the sides of the right triangle.

Mmuae Afoforo a Wobɛpaw:

Hypotenuse

Leg

Label the sides of the right triangle.

Mmuae Afoforo a Wobɛpaw:

Leg

Hypotenuse

Use the Pyhthagorean Theorem to Find the Hypotenuse when given both legs

Looking back at your work using the Pythagorean Theorem, explain the steps to find the length of the hypotenuse of a right triangle when given the lengths of both legs.(Write your steps on your white board and take picture of your board and upload the picture below)

Use the Pyhthagorean Theorem to Find A Leg when given the Hypotenuse and the other Leg

Looking back at your work using the Pythagorean Theorem, explain the steps to find a leg of a right triangle when given the lengths of the other leg and the hypotenuse. (Write your steps on your white board and take picture of your board and upload the picture below)

More Practice

Find the missing side.

Pythagorean Triples

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Find missing leg or hypotenuse of a NON-Pythagorean Triple (not mickey mouse side length)

Find the exact and approximate length of hypotenuse (non-triple)

Exact length =

Approximate length =

Find the exact and approximate length of leg (non-triple)

Exact Length =

Approximate Length =

More and more Practice Finding a missing side of a right triangle Using the Pythagorean Theorem

The lengths of the legs of a right triangle are 10 and 24. Find the length of the hypotenuse.

Hypotenuse =

A right triangle has a leg with the length of 9 and hypotenuse with a length of 13. Find the length of the other leg.

Length of the other leg =

Write in simplest radical form.

A right triangle has a leg with the length of 18 and hypotenuse with a length of 30. Find the length of the other leg.

Length of the other leg =

The lengths of the legs of a right triangle are 5 and 12. Find the length of the hypotenuse.

Hypotenuse =

A right triangle has a leg with the length of 6 and hypotenuse with a length of 10. Find the length of the other leg.

Length of the other leg =

A right triangle has a leg with the length of 11 and hypotenuse with a length of 14. Find the length of the other leg.

Length of the other leg =

Write in simplest radical form

The lengths of the legs of a right triangle are 4 and 5. Find the length of the hypotenuse.

Hypotenuse =

Write in simplest radical form

The lengths of the legs of a right triangle are 2 and 7. Find the length of the hypotenuse.

Hypotenuse =

Write in simplest radical form

Converse of the Pythagorean Theorem

CONVERSE of the Pythagorean Theorem

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Converse of Pythagorean Theorem Examples

Given the three side lengths of a triangle, determine whether the triangle is a right, acute, or obtuse triangle.

7-24-25
48-55-73
6-7-8
3-4-5
12-16-25
8-15-17
10-24-25
5-8-9
17-144-145
8-10-24
14-48-50
6-8-10
22-42-60

Right Triangle
Acute Triangle
Obtuse Triangle