the pythagorean theorem we are learning to…solve for the missing side of right triangles using the...
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a b c What Pythagoras Discovered: The area of squares built on the legs of a right triangle are equal to the sum of the area of the square built on the hypotenuse. 25 square units 9 square units 16 square units (a)(a) + (b)(b) = (c)(c) a 2 + b 2 = c 2 …this is known as the Pythagorean Theorem We can use the Pythagorean Theorem to solve for missing sides of right triangles = 25 Area of square on a leg + Area of square on a leg = Area of square on a hypotenuseTRANSCRIPT
The Pythagorean Theorem
We are learning to…solve for the missing side of right triangles using the Pythagorean Theorem.
Wednesday, May 3, 2023
The Pythagorean Theorem Right Triangle – a triangle with one right angle
Make a drawing of a right triangle. Why can a right triangle not have more than one right angle?
Hypotenuse – the longest side of a right triangle; can always be found across from the right angle on a right triangle.
Label the hypotenuse on your drawing. Leg of a Right Triangle – the two other sides of the
triangle which are not the hypotenuse Label the legs on your drawing. Hypotenus
e Leg
Leg
a
b
c
What Pythagoras Discovered:
3
4
53 5
4
The area of squares built on the legs of a right triangle are equal to the sum of the area of the square built on the hypotenuse.
25 square units
9 square units
16 square units
(a)(a)+ (b)(b)= (c)(c)
a2 + b2 = c2
…this is known as the Pythagorean Theorem
We can use the Pythagorean Theorem to solve for missing sides of
right triangles.
9 + 16 = 25
Area of square on a leg+
Area of square on a leg=
Area of square on a hypotenuse
The Pythagorean TheoremExample #1
5 cm
12 cm
?
We are looking for the hypotenuse!a2 + b2 = c2
52 + 122 = c2
25 + 144 = c2
169 = c2
2169 c13 c
The missing length of the hypotenuse is 13
centimeters long.
The Pythagorean TheoremExample #2
25 ft
24 ft ?
We are looking for a leg!a2 + b2 = c2
a2 + 242 = 252
a2 + 576 = 625
2 49a
a2 + 576 – 576 = 625 – 576
a2 = 49
a = 7
The missing length of the leg is 7 feet.
The Pythagorean TheoremExample #3
8 m
15 m
?
We are looking for the hypotenuse!a2 + b2 = c2
82 + 152 = c2
64 + 225 = c2
289 = c2
2289 c17 c
The missing length of the hypotenuse is 17
meters long.
The Pythagorean TheoremExample #4
20 in29 in
?
We are looking for a leg!a2 + b2 = c2
a2 + 202 = 292
a2 + 400 = 841
2 441a
a2 + 400 – 400 = 841 – 400
a2 = 441
a = 21
The missing length of the leg is 21 inches.
Find the length of the missing side of the right triangle below:
0 0 000
48 m
?
20 mA. 43 metersB. 50 metersC. 52 metersD. 68 metersE. I need help.
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A rectangular garden has the dimensions shown
below.
0 0 000
29 m 20 m
Find the missing length of the garden.?
A. 441 metersB. 25 metersC. 21 metersD. 35.2 metersE. I need help.
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In class, Juanita sits directly in front of Harold, 8 feet away, and directly to the left of Ian, 6 feet away.
What is the distance, in feet, from Ian to Harold?
A. 10 feetB. 14 feetC. 5.29 feetD. 100 feetE. I need help.
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