Using the Pythagorean Theorem

Using the Pythagorean Theorem

Pythagorean Theorem: a² + b² = c² If a = 20, b = x, and c = 25, then 20² + x² = 25² Evaluate 20² and 25²: 400 + x² = 625 Subtract 400 from each side: 400 - 400 +x² = 625 - 400 Simplify: x² = 225 Definition of square root: x = ±√225 Simplify: x = -15 or 15

Steps for Graphing Irrational Numbers

Using √34 as an example, that is, the hypotenuse of a triangle equal to √34 units with legs that measure 5 and 3 units, graph √34 by following these steps: STEP ONE: Find two numbers whose squares have a sum of 34 [34 = 25 + 9, or 34 = 5² + 3²]. STEP TWO: Draw a number line on grid paper. Then draw a triangle whose legs measure 3 and 5 units. STEP THREE: Adjust the compass to the length of the hypotenuse [√34 units]. Place the compass at zero [0] and draw an arc that intersects the number line. The point of intersection on the number line becomes the graph of √34. Copy and paste the following link into your browser to learn more about graphing irrational numbers on a number line: https://youtu.be/Allm58bH_co

Study Tips Related to Pythagorean Theorem

[1] In most real-world situations, only the POSITIVE (not the negative) value of the square root is considered, while working with the Pythagorean Theorem. [2] While taking tests including Pythagorean Theorem problems, look for PYTHAGOREAN TRIPLES of a 3-4-5 right triangle. For example, 25 = 5 • 5 20 = 4 • 5 x = 3 • 5 or 15