Geometry
Pythagorean Theorem Lesson (Day 1)
A. History
• An ancient Greek mathematician named Pythagoras lived from approximately 570 B.C. until 495 B.C. Although he was a philosopher and scientist, he is best known for his Pythagorean Theorem. He discovered that the sum of the squares of the two legs in a right triangle is equal to the square of the largest side, the hypotenuse. Let’s look at the numbers and formula
Pythagorean Theorem: the sum of the squares of the two legs in a triangle is equal to the square of the hypotenuse.
B. Example. In the right triangle below, locate the hypotenuse and the legs. Then define variables for them and write an equation relating all sides. Oct 5­7:43 AM
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C. How it works.
• The Pythagorean theorem relates the areas of squares drawn on the side of the right triangle
Proof: Oct 5­7:45 AM
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Oct 18­11:23 AM
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D. Examples. Find the missing side by using the Pythagorean Theorem. All Triangles are right. 2.
1.
c
c
24
15
8
3. 6
x
7
8
4. 13
23
x
Oct 5­7:46 AM
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E. Applications
5. Angle of a Ladder. A ladder with length 15 ft leans against the side of the house. From the point on the house that the ladder touches to the ground is 11 ft. How far from the house is the ladder. 6. Ryan and Joe live near one another. Ryan’s house is 4 blocks west, and 3 blocks south of Joe’s house. Without using the distance formula, find the distance between the boys’ houses. Oct 5­7:47 AM
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