i will - ms. ford's math class · i will use the pythagorean theorem and ... the converse to...
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Student Learning Objective:I will use the Pythagorean Theorem and its converse to solve problems.
I think the Pythagorean Theorem has something to with ...
Area of a square = side2Side of a square = √area
3
9
Area of a triangle = 1/2 base X height
DEFINITIONS
VAMOS A
EXPLORAR!!
Notebook page 95
Let's pause for some review!
Which of the numbers below are perfect squares??
Who is this Pythagoras guy anyway?
Years ago, a man named Pythagoras discovered an amazing fact about triangles!
If a triangle has a right angle (90 degrees)...
And you make a square on each side...
The bigger square has the exact same area as the smaller squares.
+ =
The hypotenuse is ALWAYS the longest side (largest number)!!
Let's pause and practice!!
#1 Identify the hypotenuse.
#2 Identify the hypotenuse.
15
20
25
#3 Identify the hypotenuse.
1, 2.2, 2
#4 Identify the hypotenuse.
15, 12, 19.2
#5 Identify the hypotenuse.
PYTHAGOREAN THEOREM:The sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
a2+b2=c2a
b
c
Most common Pythagorean triples:
How far is the throw from home to second?
A
B
C
90 ft.
10 ft.
30 ft.?
A 30 ft. ladder, placed 10 feet away from house, just reaches the peak of the roof. How high is the peak of the roof?
The height of a delivery truck bed is three feet. The edge of a ramp on the ground is six feet away from the truck. How long is the ramp?
If you aren't given a picture, DRAW ONE!!
Joe is on a sidewalk 100 ft. away from the tree, Jim is on a perpendicular sidewalk 70 ft. away from the tree, how far away are they from each other?
It is about 60 mi. from Dover, DE to Annapolis, MD.It is about 110 mi. from Annapolis, MD to Harrisburg, PA.About how far is it from Harrisburg, PA to Dover, DE?
It is about 130 mi. from Trenton, NJ to Harrisburg, PA.It is about 120 mi. from Harrisburg, PA to Washington D.C.About how far is it from Washington D.C. to Trenton NJ?
The Converse to the Pythagorean Theorem
If the lengths of a triangle are in the
relationship a2 + b2 = c2, THEN the triangle is a right triangle!!
Determine if the triangle below is a right triangle.
10
24
26
hypotenuse
102 + 242 = 262a2 + b2 = c2
100 + 576 = 676676 = 676
It is a r
ight
triangle
!!!
Do the following lengths form a right triangle?
***identify c FIRST!!
(draw right angle and arrow)
Do the following lengths form a right triangle?
***identify c FIRST!!
Distance in the Coordinate Plane
For example...
Step 1: Graph the points.
Step 2: Draw the RIGHT triangle.
Step 3: Label the sides of the triangle.
Step 4. Write the formula (a2 + b2 = c2).
Step 5. Fill in the given values of a and b into the formula.
Step 6. Solve for the hypotenuse (c).
Lets try together! :)
Find the distance between (5, 2) and (1, 3).
(5,2)
(1,3)
Lets try together! :)