The Pythagorean Theorem and Distance Formula
Guided Notes
Triangle Inequality Theorem: This theorem states that the ____________ of any
two sides of a triangle must be _________________ than the third side.
Side a Length
Triangle Measurements:
Side b Length
Side c Length
Angle Measure
Angle Measure
Angle Measure
1. Classify your triangle by its sides and angles:
___________________________________________________________________
2. How many tiles did you use on side a? __________________________________
How does this compare to the LENGTH of side a?
___________________________________________________________________
3. How many tiles did you use on side b? __________________________________
How does this compare to the LENGTH of side b?
___________________________________________________________________
4. Where you able to make a PERFECT square on side c? ____________________
5. Hypothesize why you believe you were or were not able to make a perfect square
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
6. Which column does YOUR triangle belong in? (Place a check mark beside your
choice)
_____ “Yes, the squares along the two shortest sides a and b combined perfectly to
make a square along the longest side c.”
_____“No, the squares along the two shortest sides a and b do not combine
perfectly to make a square along the longest side c.”
Which triangles belong in the categories below:
“No, the squares along the two shortest sides a and b do not combine perfectly to
make a square along the longest side c.”
a2  b2  c2
a2  b2  c2
Based on what we just discovered, we know that:
a2  b2  c2
a2  b2  c2
a2  b2  c2
You have just discovered THE PYTHAGOREAN THEOREM!
a2  b2  c2
It states that the _____________ of the ________________ of the two shorter sides
of a ________________ triangle is _________________ to the
_________________ of the longer side.
Vocabulary Check
Identify the name of each part of the right triangle below
ZZZZ
Pythagorean Theorem Practice
2
2
2
4

5

c
1.
2.
3.
3.
4. The Irrational Club wants to build a tree house.
They have a 9foot ladder that must be propped diagonally against the tree. If the
base of the ladder is 5 feet from the bottom of the tree, how high
will the tree house be off the ground?
Now that we have officially learned how to use the Pythagorean Theorem, we can now use it to
find the distance between two points on a coordinate plane!
You should remember finding vertical and horizon
Example: Find the distance between (-2,4) and (-5,-6)
Plot each of the points on the coordinate grid below.
The distance between 4 and -6 is the _________________________ distance
The distance between -2 and -5 is the _________________________ distance
So how can I find the distance between the two points?
Horizontal Distance: -2 – (-5) = _________
Vertical Distance: 4 – (-6) = ________
Distance between the two points = ?
32 102  _____
____________________ Distance
____________________ Distance
*Use the Pythagorean Theorem to solve the equation!*
Distance Formula Practice
1.
2.