Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph...
-
Upload
maria-patricia-holland -
Category
Documents
-
view
214 -
download
0
Transcript of Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph...
![Page 1: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/1.jpg)
Pythagorean Theorem
![Page 2: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/2.jpg)
Bell Work□Please graph the problem and the answer: 9² + 12² =
□Graph the problem on one paper and the answer on the other paper. See my Example on the board.
![Page 3: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/3.jpg)
Pythagorean Theorem -
□In right triangles, the square of the length of the hypotenuse is equal to the sum of the squares of its legs.
□a² + b² = c²
![Page 4: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/4.jpg)
Right Triangle□right triangle –triangle that has one
right angle □leg – the two sides of a right triangle
that form a right angle□right angle – an angle that measures
90º□hypotenuse – the side of a right
triangle that is opposite the right angle; the longest side of a right triangle
![Page 5: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/5.jpg)
hypotenuseleg
leg
right angle
90°
![Page 6: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/6.jpg)
Who can find the Right Triangles?
![Page 7: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/7.jpg)
Is the triangle Right?Using the Pythagorean Theorem,
determine which of the following would be right triangle.
a.18 feet, 24 feet, 30 feetb.3 miles, 4 miles, 5 milesc.11 inches, 13 inches, 17 inches
![Page 8: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/8.jpg)
Converse□If you reverse the parts of the
Pythagorean Theorem, you have formed its converse. The converse of the Pythagorean Theorem is also true.
□EX: c² = a² + b²□if the sides of a triangle have lengths
a, b and c so that c² = a² + b², then the triangle is a right triangle.
![Page 9: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/9.jpg)
Example:□The hypotenuse of a right triangle is 15 feet and leg a is 12 feet. What is the length of leg b?
![Page 10: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/10.jpg)
Pythagorean Triples
□A set of three integers that satisfy the Pythagorean Theorem.a b c Check a² + b² =
c²
original
3 4 5 9 + 16 = 25
x2 6 8 10 36 + 64 = 100
x3 9 12 15 81 + 144 = 225
x4 12 16 20 144 + 256 = 400
x5 15 20 25 225 + 400 = 625
![Page 11: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/11.jpg)
Who uses the Pythagorean
Theorem?□Cartographers (map makers)
□Surveyors□Designers□Architects□Pilots
□Sailors□Astronomers□Astronauts□Construction Workers
□Oceanographers
![Page 12: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/12.jpg)
Do I use the Pythagorean
Theorem?□Which path is the quickest?
1 mile
2 miles
2 miles
1 mile
![Page 13: Pythagorean Theorem. Bell Work □ Please graph the problem and the answer: 9² + 12² = □ Graph the problem on one paper and the answer on the other paper.](https://reader036.fdocuments.us/reader036/viewer/2022070400/56649e6f5503460f94b6c4b2/html5/thumbnails/13.jpg)