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DO NOW!
4
2
+5
2
=c
2
Solve.Evaluate.
6
2
+7
2
3
2
+8
2
=c
2
7
2
+10
2
=c
2
11
2
+6
2
=c
2
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LESSON 24: PYTHAGOREAN THEOREM
STANDARDS: 7.G.5, 7.G.6, 7.G.8, and 7.G.9
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Can you identify all parts of a right triangle?
leg
leg
right angle
hypotenuse
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Word Description
The sides of a right triangle thatshare the 90 degree angle.
The side of a right triangle that isopposite the 90 degree
angle.
The sum of the squares of the legs isequal to the square of
thehypotenuse.
Legs
Pythagorean
Theorem
Hypotenuse
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Identify the legs and the hypotenuse
hypotenuselegs
a
cb
b
a
c
c
ba
cb
a
cba cba
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What do you notice?
Find the area of each square.
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Can you arrange the blue and pink squares inside the yellow
square?
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The Pythagorean Theorem
a2
+ b2
= c2
TOUCH
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In right triangles,
the square of thelength of thehypotenuse is
equal to the sum ofthe squares of thelengths of the legs.
a2
+ b2
= c2
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Identify the hypotenuse in each triangle
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What is the Pythagorean Theorem?
Label the following triangle, according the theorem.
What is the equation?
hypotenuse
bc
leg
lega
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What is Pythagorean Theorem?
How do we use Pythagorean Theorem?
Pythagorean Theorem is a rule that helps findthe distance or
measure of one side of a right
triangle when two measures are known.
Substitute the measures into thePythagorean Theorem,use Algebra
to solve the equation.
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For which triangles does the Pythagorean theorem apply?
4
1 2
3
5
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Using the Pythagorean Theorem
3
4
Example 1:Find the unknown measurement. Refer to the
diagram!
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Example 2:Find the unknown measurement.Refer to the diagram.
15 12
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What happens when you try to find thesquare root of a
'non-perfect' square?
For example, what is the square root of 41?
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5cm
6 cm
c
Step 1:
a = 5b = 6c = x
Step 2:
a2
+ b2
= c2
52
+ 62
= x2
25 + 36 = x2
61 = x2
Using the Pythagorean theorem, it is possible, knowing thelength
of sides a and b, to figure out the length of side c.
Step 3
61 = x2
61 = x
7.81 = xx = c =7.81 cm
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1.
2cm
2 cm
2.
2cm
6 cm
___ cm
Find the missing lengths!
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a b c a2 b2 c2 a2+b
5 12 13 25 144 169 169
8 15 17 64 225 289 289
10 6.3 12 100 39.69 144 139.69
10 6 11.3 100 36 127.69 136
6 8 10 36 64 100 100
Copy and complete!
NOTRIGHTTRIANGLES
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1.
4cm
1 cm
2.
3cm
5 cm
___ cm___ cm
3.
1
cm
1 cm
4.
2cm
6 cm
___ cm___ cm
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One end of a ladder is placed 7 feet from a a house.The other of
the ladder reaches 20 feet up the side ofthe house. How long is the
ladder?
Place all items in the proper place on the houseaccording to the
story above.
20 ft
7 ft
?
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12 ft
43 ft
How high off the ground is the owl?
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LEARNING LOG - 7.G.8 - NickiNicki is unsure how to find the
missing value. Can youhelp her? Explain your reasoning and show all
work.
3cm ___ cm
8 cm
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a = 8
c = 12b = 8 b = 12
c = 13
a = 5
Considering the three side measurements (a, b, and c), which of
the followingtwo triangles is a right triangle?
Triangle 1 Triangle 2
A right triangle can be found whenever the Pythagorean Theorem
is true.
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Which of these triangles are right triangles?
11.3 yards
10y
ards
6yard
s
8 meters
10m
eters
6me
ters
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LEARNING LOG - 7.G.9 - Is it a Right Triangle?
5
inc
hes
4inches
6in
ches
Is this a right triangle? How can you tell?Explain and show
proof.
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How do we find a missing leg?!
3
5
b
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a2
+ b2
= c2
82
+ 62
= c2
64 + 36 = 100100 = c
2
c = 10
a2
+ b2
= c2
52
+ y2
= 82
25 + y
2
= 64
y2
= 39
Length of the hypotenuse Length of a leg
6
8c
5
8
y
Find the missing lengths
![LESSON 30: Pythagorean Theorem Part 1 [OBJECTIVEntnmath.kemsmath.com/Level H Lesson Notes/Grade 8- Lesson 30... · LESSON 30: Pythagorean Theorem Part 1 [OBJECTIVE] The student will](https://img.dokumen.tips/doc/110x75/5af770497f8b9a9e5990bc97/lesson-30-pythagorean-theorem-part-1-h-lesson-notesgrade-8-lesson-30lesson.jpg)
