11
Pyth T per 1.notebook 1 November 30, 2015 Lesson 13 Pythagorean Theorem Pythagorean Theorem
Pyth T per 1.notebook
1
November 30, 2015
Lesson 13Pythagorean Theorem
Pythagorean Theorem
Pyth T per 1.notebook
2
November 30, 2015
Discovering the Pythagorean Theorema) On grid paper, draw a right triangle. 1)right angle2) no longer than 5 units 3) 3 different measurements
b) Label the longest side opposite the right angle c.
c) Label the two shorter sides a and b.
d) Draw squares along each of the three sides.
e) Cut out the three squares.
f) Draw eight more of the same right triangle.
g) Arrange the figures to form two identical larger squares.
Figure Layout
What do you notice now that you've created these congruent squares?
Pyth T per 1.notebook
3
November 30, 2015
http://www.youtube.com/watch?v=uaj0XcLtN5cProving the Pythagorean Theorem in TWO MINUTES:
Pythagorean Theorem a2 + b2 = c2
It describes the relationship between the length of the legs and
hypotenuse for any right triangle.
leg
leg
hypotenuse
Guided practice p. 164 #14
Why is it important to figure our which side is the hypotenuse first?
1) Which side is the hypotenuse? 2) a2 + b2 = c2 (leg + leg = hypotenuse)
Pyth T per 1.notebook
4
November 30, 2015
Pythagorean Theorem a2 + b2 = c2
It describes the relationship between the length of the legs and
hypotenuse for any right triangle.
Take out all the pages for lesson 13 and look at Exercise 1.
Let's apply what we've learned about the Pythagorean Theorem:
1) Which side is the hypotenuse? 2) a2 + b2 = c2 (leg + leg = hypotenuse)
Pyth T per 1.notebook
5
November 30, 2015
Assignment: ENY 3.13 PS #15
Complete the Exit Ticket independently.
http://www.youtube.com/watch?v=w0dF1zUU9tE
Another way to prove the Pythagorean Theorem:
Pyth T per 1.notebook
6
November 30, 2015
More Pythagorean Theorem
and Real World Situations
15 ft
a
2.9 cm
8 ftc2.1 cm
Pyth T per 1.notebook
7
November 30, 2015
Real World SituationsA tennis play asks the referee a question. The sound of the player's voice travels only 30 feet. Can the referee hear the question? Explain.
Real World SituationsYou are playing capture the flag. You are 50 yards north and 20 yards east of your team's base. The other team's base is 80 yards north and 60 yards east of your base. How far are you from the other team's base?
Pyth T per 1.notebook
8
November 30, 2015
Real World SituationsA box has a length of 6 inches, a width of 8 inches, and a height of 24 inches. Can a cylindrical rod with a length of 63.5 centimeters fit in the box? Explain your reasoning.(Hint: How many cm = in) 1 in = 2.54 cm
Assignment: BI 7.3 #117 odd
A boy in a wheelchair was going up a ramp that was 10 feet long, but the distance on the ground was 8 feet. How high is the wheel chair ramp?
Complete the Exit Ticket independently.
Pyth T per 1.notebook
9
November 30, 2015
Use the Pythagorean Theorem to find the missing sides. Round the value to the nearest hundredth if you need to.
A right triangle has 2 legs that are 27mm and 16mm. What is the length of the third side?
A right triangle has one leg that is 4.5 in. and a hypotenuse that is 7.6 in. What is the length of the third side?
Converse
of
Pythagorean Theorem
What do you think the converse is?
Pyth T per 1.notebook
10
November 30, 2015
34 ft
16 ft
30 ft
Converse of the Pythagorean Theorem
If the sides of a triangle have lengths a, b, and c that a2 + b2 = c2, then the triangle is a right triangle.
In other words, if the three sides of a triangle are put into the Pythagorean Theorem and it is a true statement, then the triangle is a right triangle.
Pyth T per 1.notebook
11
November 30, 2015
1) Which side is the hypotenuse? 2) a2 + b2 = c2
Take out all the pages for Lesson 14.
Assignment: ENY 3.14 #16
Complete the Exit Ticket independently.
