Download 01-12-17 Pythagorean Theorem Notes

1/17/2017
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Upcoming Dates
• 1/16 (Mon)
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Unit 7
SCHOOL HOLIDAY
Major Quiz on Triangles
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Angles in Triangles
Pythagorean Theorem
(Angles & Pythagorean Theorem)
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Unit 7: Words To Know
• Right triangle – triangle with 1 right angle and
2 acute angles
• Legs of a right triangle – 2 shortest sides of a
right triangle; sides that form the right angle
• Hypotenuse – longest side of right triangle;
side opposite the right angle
On your graph paper:
• Draw a right triangle in the center with legs of 3
units and 4 units.
• Draw a square that has a side length of 3 units in
the lower left corner. Write its area inside.
• Draw a square that has a side length of 4 units in
the lower right corner. Write its area inside.
• Add the 2 areas together, and draw a square
with that area in the top right corner.
Pythagoras
• Born in Greece in 569 B.C.
• Is known as the Father of Numbers.
• Traveled extensively in Egypt, learning math,
astronomy, and music.
• Urged citizens of Croton to follow his religious,
political, and philosophical goals.
• His followers were known as Pythagoreans. They
had to observe a rule of silence for five years before
they could contribute to the group. Breaking this
silence was punishable by death!
The sum of the squares of the shortest
sides is equal to the square of the
longest side.
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1/17/2017
Pythagorean Theorem
Is it a right triangle?
• Used to find a missing side length of a RIGHT
triangle.
𝑎 = 5, 𝑏 = 12, 𝑐 = 13
Hypotenuse
𝑎 = 7, 𝑏 = 8, 𝑐 = 12
Legs
𝑎2 + 𝑏2 = 𝑐 2, where 𝑎 and 𝑏 are legs,
and 𝑐 is the hypotenuse
Reminder: The inverse operation of a
square (𝑥 2 ) is a square root ( 𝑥).
Is it a right triangle?
𝑎 = 6, 𝑏 = 8, 𝑐 = 10
12 cm
𝑥
35 cm
𝑎 = 4, 𝑏 = 8, 𝑐 = 9
28 m
35 m
𝑥
24 in
25 in
𝑥
12 in
𝑥
16 in
2