Pythagorean Geometry

A Pythagorean triple consists of three positive integers a, b, and c, such that a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup>. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1).  A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle, and is necessarily a right triangle.

Questions on basic geometry and Pythagorean geometry are on most high school tests

Practice Questions

1. What is the length of each side of the indicated square above?

a. 10
b. 15
c. 20
d. 5

2. What is the length of the sides in the triangle above?

a. 10
b. 20
c. 100
d. 40

3. For the given diameter, what is the square of the indicated measurement?

a. 6
b. 72
c. 36
d. 64

4. Every day starting from his home Peter travels due east to the school. After school he travels due north to the library. This way Peter travels 25 kilometers. What is the distance between Peter’s home and the library?

a. 15 km
b. 10 km
c. 5 km
d. 12 ½ km

5. What is the length of the missing side in the triangle above?

a. 6
b. 4
c. 8
d. 5

Answer Key

Written by, Brian Stocker MA., Complete Test Preparation Inc.

Date Published: Wednesday, February 13th, 2019
Date Modified: Wednesday, April 10th, 2019
Brian Stocker

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    2 Comments

  1. Tom
    March 30, 2019
    Reply

    I’m confused by question 4. In the answer you say a squared + b squared = 25. Isn’t 25 just the sum of a and b, not those squared?

    • Brian Stocker
      April 1, 2019
      Reply

      The Pythagorean formula is the SUM of a and b – a2 + b2 = c2

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