Transcript of Applying the Pythagorean Theorem Adapted from Walch Education.
- Slide 1
- Slide 2
- Applying the Pythagorean Theorem Adapted from Walch
Education
- Slide 3
- Key Concepts Reviewing Distance on a Number Line To find the
distance between two points, a and b, on a number line, find the
absolute value of the difference of a and b. This can be expressed
algebraically as |a b| or |b a|. For example, to find the distance
between 4 and 5, take the absolute value of the difference of 4 and
5. |4 5| = |9| = 9 or |5 4| = |5 + 4| = |9| = 9 The distance
between the numbers 4 and 5 is 9 units.
- Slide 4
- Reviewing the Pythagorean Theorem Right triangles are triangles
with one right (90) angle. The side that is the longest and is
always across from the right angle is called the hypotenuse. The
two shorter sides are referred to as the legs of the right
triangle. We can use the Pythagorean Theorem to calculate the
length of any one of the three sides.
- Slide 5
- To find the distance between two points on a coordinate system,
we can use the Pythagorean Theorem. Finding the Distance Between
Two Points Using the Pythagorean Theorem 1.Plot the points on a
coordinate system. 2.Draw lines to form a right triangle, using
each point as the end of the hypotenuse. 3.Calculate the length of
the vertical side, a, of the right triangle by taking the absolute
value of the difference of the y-values ( |y 2 y 1 | ). 4.Calculate
the length of the horizontal side, b, of the right triangle by
taking the absolute value of the difference of the x- values ( |x 2
x 1 | ). 5.Use the Pythagorean Theorem to calculate the length of
the hypotenuse, c.
- Slide 6
- Practice # 1 Tyler and Arsha have mapped out locations for a
game of manhunt. Tylers position is represented by the point (2,
1). Arshas position is represented by the point (7, 9). Each unit
is equivalent to 100 feet. What is the approximate distance between
Tyler and Arsha?
- Slide 7
- Calculate the length of the vertical side, a, of the right
triangle. |y 2 y 1 | = |9 1| = |8| = 8 Calculate the length of the
horizontal side, b, of the right triangle. |x 2 x 1 | = |7 2| = |5|
= 5
- Slide 8
- Use the Pythagorean Theorem to calculate the length of the
hypotenuse, c. a 2 b 2 = c 2 Pythagorean Theorem 8 2 + 5 2 = c 2
Substitute values for a and b. 64 + 25 = c 2 Simplify each term. 89
= c 2 Simplify. Take the square root of both sides of the equation.
The distance between Tyler and Arsha is approximately 9.4 units or
940 feet.
- Slide 9
- Practice # 2 Kevin is standing 2 miles due north of the school.
James is standing 4 miles due west of the school. What is the
distance between Kevin and James?
- Slide 10
- Thanks for Watching!!!! ~ Ms. Dambreville