Pythagorean Theorem 8th Math Presented by Mr. Laws

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Presentation transcript:

Pythagorean Theorem 8th Math Presented by Mr. Laws Geometry Pythagorean Theorem 8th Math Presented by Mr. Laws A2 + B2 = C2 c a b

Standard 8.G.7 – Real world application of Pythagorean theorem: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Essential Question How does the Pythagorean Theorem Formula help you find the unknown side lengths of a right triangles in real-world or mathematical problems?

Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as a means to understand the natural world First to teach that the earth was a sphere that revolves around the sun

Right Triangle Hypotenuse (c) is on the opposite side of the right angle and is the longest side of the right triangle. Legs are the side a and b of a right triangle. Leg (a) 900 Symbol for right triangle Leg (b) Pythagoras developed a formula for finding the length of the sides of any right triangle.

Pythagorean Theorem Formula b c a2 + b2 = c2 C2 32 + 42 = 52 A2 9 + 16 = 25 B2

Finding the Hypotenuse (c) Model # 1 c2 = a2 + b2 c2 = 32 + 42 ? 3 a c2 = 9 + 16 c c2 = 25 𝒄𝟐 = 𝟐𝟓 b 4 c = 5

Finding the Leg (a) 10 ? 𝒂𝟐 = 𝟑𝟔 a = 6 8 Model # 2 a2 = c2 - b2 𝒂𝟐 = 𝟑𝟔 b a = 6 8

Finding the Leg (b) 20 12 𝒃𝟐 = 𝟐𝟓𝟔 b = 16 ? Model # 3 b2 = c2 - a2 𝒃𝟐 = 𝟐𝟓𝟔 b b = 16 ?

Finding missing sides 7 15 𝒃𝟐 = 𝟏𝟕𝟔 𝒃 ≈𝟏𝟑.𝟑 What steps will you take to find the missing side? b2 = c2 - a2 7 15 b2 = 152 - 72 b2 = 225 - 49 b2 = 176 𝒃𝟐 = 𝟏𝟕𝟔 𝒃 ≈𝟏𝟑.𝟑 Round to the nearest tenth

Using Pythagorean Theorem to Prove Right Triangles You know that Pythagorean Theorem formula works with all right triangles, We can use the converse of this theorem, which is: if a2 + b2 = c2, then the triangle is a right triangle. 5 cm 12 cm 13 cm Is this a right triangle? a2 + b2 = c2 52 + 122 = 132 25 + 144 = 169 169 = 169 Yes, this is a right triangle!

Using Pythagorean Theorem to Prove Right Triangles You know that Pythagorean Theorem formula works with all right triangles, We can use the converse of this theorem, which is: if a2 + b2 = c2, then the triangle is a right triangle. 6 cm 8 cm 9 cm Is this a right triangle? a2 + b2 = c2 62 + 82 = 92 36 + 64 = 81 𝟏𝟎𝟎≠𝟖𝟏 No, this is not a right triangle!

Pythagorean Triple Three numbers can be called a Pythagorean triple if a2 + b2 = c2 and all the numbers are integers (positive whole numbers). Examples: a2 b2 c2 3 4 5 6 8 10 12 13 7 24 25 9 15 26

SUMMARY Can you answer the essential question with confidence and a clear understanding of the lesson. What are some key concepts you should remember about the Pythagorean Theorem Is there more you need to learn about this lesson?