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Learning Math Home
Session 6, Part C: Applications of the Pythagorean Theorem
Session 6 Part A Part B Part C Homework
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Session 6 Materials:

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:


1 foot


2 feet


10 feet


n feet

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
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.


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

Next > Part C (Continued): The Distance Formula

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