Bell Work. 11-3 D/E The Pythagorean Theorem Students will be able to understand and apply the Pythagorean Theorem.

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Presentation transcript:

Bell Work

11-3 D/E The Pythagorean Theorem Students will be able to understand and apply the Pythagorean Theorem.

Explore the Pythagorean Theorem.

Analyze the Results

In a right triangle, sides have special names…

The Pythagorean Theorem Describes the relationship between the length of the hypotenuse and the lengths of the legs.

Remember The Pythagorean Theorem ONLY works on RIGHT TRIANGLES!!!

Steps to Using the Pythagorean Theorem 1.Label your sides (a, b, and c) on the triangle. 2.Write out the Pythagorean Theorem. 3.Plug in the side lengths for a, b, and c. 4.Square the sides. 5.Solve/Simplify.

Find the Length of the Hypotenuse *Check: Does your answer make sense? Remember the hypotenuse is ALWAYS the longest side.

Find the Length of the Hypotenuse

Check Your Progress

Pythagorean Theorem Rap! RHQWE

Real-World Example A scuba diver dove 14 feet below the surface. Then he swam 16 feet horizontally. How far is the diver from his boat?

Check Your Progress

Finding the Length of a Leg

Check Your Progress

Common Pythagorean Triples There are special integer relationships based on the Pythagorean Theorem, known as Pythagorean Triples. All Pythagorean Triples can be verified using the Pythagorean Theorem. Some common ones are: 3:4:5 5:12:13 8:15:17 7:24:25 All multiples of these are also Pythagorean Triples. For example, 9:12:15 is fond by multiplying all sides of a 3:4L5 triangle by 3.

Check Your Progress

Rally Coach- Check Your Understanding pg 658 * Complete on a sheet of paper to be turned into the bin at the end of class!

11-3F Distance on a Coordinate Plane Students will be able to find the distance between two points on the coordinate plane.

Explore

How to find a distance on a coordinate plane 1.Plot the given points on graph paper 2.Draw a line segment between the two points. 3.Form a right triangle then, find the lengths of the legs of the triangle. 4.Apply the Pythagorean Theorem to find the length of the hypotenuse!

Example- Find the distance Can a length be negative? No! Use only the positive result

Check Your Progress Find the distance between the points (-3,2) and (4, -1) Round to the nearest tenth if necessary.

You Try- Draw a picture!

Check your understanding pg 662 * Complete on same sheet of paper to be turned into the bin at the end of class!

Homework Workbook pages 179 and 181 ODD Early finishers can work on missing assignments or read a book! *Make sure you turned your classwork into the orange bin!