Session 6, Part C: Applications of the Pythagorean Theorem

Session 6, Part C:
Applications of the Pythagorean Theorem (35 minutes)

In This Part: Finding Missing Lengths | The Distance Formula

The Pythagorean theorem is useful for finding missing lengths. If you can find a right triangle in a picture, you can often find the length you need. All you need to know is that if a² + b² = c², then That is, you can take the square root of both sides of the equation. Because you're working with lengths (so all the values are positive), you can find c.

Problem C1

Find the length of the diagonal of a square whose sides have the following lengths:

a.	1 foot
b.	2 feet
c.	10 feet
d.	n feet

Draw a picture and look for right triangles. Close Tip

Problem C2

Find the lengths of all the segments that are not labeled in the picture below. Describe a pattern in the lengths.

Problem C3

The perpendicular bisector of a segment is perpendicular to the segment and goes through the midpoint. Show that any point on the perpendicular bisector of a segment is the same distance from each of the endpoints.

The line is the perpendicular bisector of AB. Use the Pythagorean theorem to explain why PA and PB (the dashed segments) are the same length.

Next > Part C (Continued): The Distance Formula

Session 6: Index | Notes | Solutions | Video