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 Draw a picture and look for right triangles!

 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.

 Problems C1-C3 adapted from Connected Geometry, developed by Educational Development Center, Inc. pp. 65, 205, 206. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math
 Session 6: Index | Notes | Solutions | Video