Post on 12-Jan-2016
Developer’s name: Ahmed Fallatah
03/17/2013
ETEC 544 Instructor: Brian Newberry
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a2 + b2 = c2
Instruction
To use this product effectively please follow the instruction below:
• Read carefully each screen and understand the contents.
• Do the practice that included in the product.
• Use the Bar at the bottom of the screen to navigate the product.
• Use the next button to go to next screen.
• The time supposed to complete the project is 40 to 50 minutes.
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a2 + b2 = c2
Objectives
After working on the product you will be able to:
Identify a right triangle.
Using the Pythagorean Theorem to calculate the
lengths of the hypotenuse of a right triangle.
Calculate any missing leg of a right triangle.
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
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a2 + b2 = c2
Who is Pythagoras? Pythagoras was a Greek mathematician and
a philosopher, but he was best known for his
Pythagorean Theorem. He was born around 572 B.C. on the island of Samos. For
about 22 years, Pythagoras spent time traveling though Egypt and Babylonia to
educate himself.
Pythagoras excelled in many subjects, such as music, medicine and
mathematics. Pythagoras made influential contributions to philosophy and
religious teaching in the late 6th century BC.
He is often revered as a great mathematician, mystic and scientist, but he is
best known for the Pythagorean Theorem which bears his name.
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
NEXT
a2 + b2 = c2
What is Pythagorean Theorem?
Pythagorean Theorem states that the square of the hypotenuse C is equal to the squares
of the two sides of the triangle A and B , or A2 + B2 = C2, where C is the hypotenuse.
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
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AB
c
Press the action button to see how the equation is formulated
a2 + b2 = c2
Real Examples
Imagine that, You're locked out of your
house and the only open window is on
the second floor, 25 feet above the
ground. You need to borrow a ladder
from one of your neighbors. There's a
bush along the edge of the house, so
you'll have to place the ladder 10 feet
from the house.
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
NEXT26.93 feet
What length of ladder do you need to reach the window?
a2 + b2 = c2
Right triangle and hypotenuse
Right triangle is a triangle containing an angle of 90 degrees.
The hypotenuse of a right triangle is the triangle's longest side. Or it is the
side opposite the right angle.
Not Right triangle
Hypotenuse
90 degrees angle
Right triangle
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
NEXT
a2 + b2 = c2
Example 1
Find the unknown length for the triangleShown, A = 3 , b =4
a2 + b2 = c2
The square of a (a²) plus the square of b (b²) is
equal to the square of c (c²)
32 + 42 = 52
9 + 16 = 25
C = 25
C = 5
ANSWER
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
NEXT
a2 + b2 = c2
Example 2Find the unknown length for the triangle
Shown, A = 3 , b =4
a2 + b2 = c2
52 + 122 = c2
25 + 144 = c2
169 = c2
c2 = 169
c = √169
c = 13
ANSWER
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
NEXT
a2 + b2 = c2
Practice 1
Now it is your turn to solve this problem.
Does the triangle with the given side lengths is
a right triangle?
Does a2 + b2 = c2?
No the triangle is not a right triangle
Yes the triangle is a right triangle because c2 = 676
Yes the triangle is a right triangle because c2 = 525
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
Please choose the right answer
a2 + b2 = c2
a2 + b2 = 102 + 242 = 100 + 576 = 676
And
c2 = 262 = 676
Yes the triangle is a right triangle?NEXT
a2 + b2 = c2
The answer is wrong, please try again.
Go Back
a2 + b2 = c2
The answer is wrong, please try again.
Go Back
a2 + b2 = c2
Identifying any missing leg
To calculate any missing leg of a right triangle we use the same equation with
different formula. We use subtract to find the value of the missing leg for
Example:
a2 + b2 = c2
92 + b2 = 152
81 + b2 = 225
225 - 81 = b2
b2 = 144
b = √144
b = 12
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
NEXT
a2 + b2 = c2
Practice 2
in this triangle what is the value of b?
a2 + b2 = c2
42 + b2 = 52
b2 = 52 _ 42
A 4
B
C 5
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
b = 4 b = 3
Please choose the right answer
a2 + b2 = c2
b2 = 15 _ 16
b2 = √9
b = 3
The answer is right
NEXT
A 4
B 3
C 5
a2 + b2 = c2
The answer is wrong, Please try again.
Go Back
a2 + b2 = c2
Review
Pythagorean Theorem is theory used to find side lengths of right
triangle.
The equation of the Pythagorean Theorem is a2 + b2 = c2
Right triangle is a triangle containing an angle of 90 degrees.
The hypotenuse of a right triangle is the triangle's longest side. Or it is
the side opposite the right angle.
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle
NEXT
a2 + b2 = c2
Thank you
objectives Pythagoras Pythagorean Theorem
Real Examples Example 1 Example 2 Practice 1 Identifying any
missing leg Practice 2 ReviewRight triangle