7.4 NOTES
Pythagorean Theorem and Distance Formula
Name __________________________
Pythagorean Theorem: If a triangle is a right triangle, then 𝑎2 + 𝑏 2 = 𝑐 2 .
Converse of the Pythagorean Theorem: If 𝑎2 + 𝑏 2 = 𝑐 2 , then the triangle is a right triangle.
Label the right triangle with the
following: a , b , c , leg, leg, and
hypotenuse
Determine the length of the
missing side of the right
triangle.
Determine the length of the
missing side of the right
triangle.
Determine if each triangle is a right triangle.
Distance Formula:
The points (1,2) and (3,7) are shown on the coordinate plane.
1. Draw a line between the two points.
2. Draw a right triangle so that the line between the points is
the hypotenuse of the right triangle.
3. Determine the length of the horizontal leg. ____________
4. Determine the length of the vertical leg. ______________
5. Use the Pythagorean Theorem to determine the distance
between the two points.
Distance ________
6. How do the lengths of the legs relate to the slope of the
hypotenuse?
The horizontal leg is the ___________________________________________________
the vertical leg is the _____________________________________________________
The DISTANCE FORMULA states that if (x1,y1) and (x2,y2) are two points on the coordinate plane,
then the distance (d) between (x1,y1) and (x2,y2) is given by 𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
(x2,y2)
Length of vertical leg
y2 - y1
Pythagorean Theorem
(x1,y1)
𝑐 2 = 𝑎2 + 𝑏 2
𝑐 = √𝑎2 + 𝑏 2
Length of
horizontal leg
𝑐 = √(ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑙𝑒𝑔)2 + (𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑙𝑒𝑔)2
x2 - x1
Together as a class
Find the distance between the two points.
By yourself
Find the distance between the two points.
Find the distance between the two points.
(2, 8) (10,2)
Find the distance between the two points.
Find the distance between the two points.
Find the distance between the two points.