warm up solve the first 4 questions on your worksheet
TRANSCRIPT
![Page 1: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/1.jpg)
Warm Up
Solve the first 4 questions on your worksheet.
![Page 2: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/2.jpg)
Pythagoras and the
Pythagorean Theorem
![Page 3: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/3.jpg)
Biography of Pythagoras
•Pythagoras was a Greek mathematician and a philosopher, but was best known for his Pythagorean Theorem.
•He was born around 572 B.C. on the island of Samos.
• For about 22 years, Pythagoras spent time traveling though Egypt and Babylonia to educate himself.
•At about 530 B.C., he settled in a Greek town in southern Italy called Crotona.
•Pythagoras formed a brotherhood that was an exclusive society devoted to moral, political and social life. This society was known as Pythagoreans.
![Page 4: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/4.jpg)
Biography of Pythagoras• The Pythagorean School excelled in many
subjects, such as music, medicine and mathematics.
• In the society, members were known as mathematikoi.
• History tells us that this theorem has been introduced through drawings, texts, legends, and stories from Babylon, Egypt, and China, dating back to 1800-1500 B.C.
• Unfortunately, no one is sure who the true founder of the Pythagorean Theorem is. But it does seem certain through many history books that some time in the sixth century B.C., Pythagoras derives a proof for the Pythagorean Theorem.
![Page 5: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/5.jpg)
Right Triangles
• Longest side is the hypotenuse, side c (opposite the 90o angle)
• The other two sides are the legs, sides a and b
• Pythagoras developed a formula for finding the length of the sides of any right triangle
![Page 6: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/6.jpg)
The Pythagorean Theorem
“For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.”
aa22 + b + b22 = c = c22
![Page 7: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/7.jpg)
The Pythagorean Theorem• The sum of the squares of
each leg of a right angled triangle equals to the square of the hypotenuse
a² + b² = c²
![Page 8: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/8.jpg)
![Page 9: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/9.jpg)
Applications• The Pythagorean theorem has far-reaching
ramifications in other fields (such as the arts), as
well as practical applications.
• The theorem is invaluable when computing
distances between two points, such as in navigation
and land surveying.
• Another important application is in the design of
ramps. Ramp designs for handicap-accessible sites
and for skateboard parks are very much in demand.
![Page 10: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/10.jpg)
![Page 11: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/11.jpg)
Baseball Problem
A baseball “diamond” is really a square.
You can use the Pythagorean theorem to find distances around a baseball diamond.
![Page 12: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/12.jpg)
Baseball Problem
The distance between consecutive bases is 90feet. How far does a catcher have to throwthe ball from home plate to second base?
![Page 13: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/13.jpg)
Baseball Problem
To use the Pythagorean theorem to solve for x, find the right angle.
Which side is the hypotenuse?
Which sides are the legs?
Now use: aa22 + b + b22 = c = c22
![Page 14: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/14.jpg)
Baseball ProblemSolution
• The hypotenuse is the distance from home to second, or side x in the picture.
• The legs are from home to first and from first to second.
• Solution: x2 = 902 + 902 =
16,200 x = 127.28 ft
![Page 15: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/15.jpg)
Ladder Problem
A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window?
![Page 16: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/16.jpg)
Ladder ProblemSolution
• First draw a diagram that shows the sides of the right triangle.
• Label the sides: – Ladder is 25 m– Distance from
house is 7 m
• Use a2 + b2 = c2 to solve for the missing side. Distance from house: 7 meters
![Page 17: Warm Up Solve the first 4 questions on your worksheet](https://reader035.vdocuments.mx/reader035/viewer/2022070404/56649f385503460f94c54704/html5/thumbnails/17.jpg)
Ladder ProblemSolution
72 + b2 = 252
49 + b2 = 625 b2 = 576 b = 24 m
How did you do? A = 7 m