Chapter 9 Real Numbers and the Pythagorean Theorem
Lesson Outline
9.2 The Pythagorean Theorem – We learned to identify right triangles and use the Pythagorean Theorem. The Pythagorean Theorem states that in any right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. We learned that the longest side of each triangle is always the side that is not part of the right angle. The theorem is named for the Greek mathematician Pythagoras who lived about 580 to 500 BC. There is evidence that 1500 years earlier the Babylonians knew the properties of this theorem. An ancient Hindu handbook for Temple builders written around 600 BC states the theorem as well. Pythagoras gets credit because he was the first to demonstrate the truth of the theorem.
We found the length of the hypotenuse in several problems when we were given the two sides adjacent to the right angle in the triangle. Then we found the missing side adjacent to the right angle when we were given the other side and the hypotenuse.
Chapter 10 Summary and Review – We completed the review section where we practiced writing an equation of a line satisfying the given conditions using the slope-intercept form. Then we practiced writing an equation of a line that passes through a given point and is either parallel or perpendicular to the graph of a given equation. Next we practiced finding the midpoint of a line.
Chapter 9 Real Numbers and the Pythagorean Theorem
Lesson Outline
9.1 Finding Square Roots – We learned to find and simplify square roots of numbers. Then we discovered that a positive number has two square roots. Next we determined that there is no square root of a negative number because the product of any two nonzero numbers must be positive. Then we practiced estimating a square root between two perfect squares. Next we practiced classifying real numbers. We learned that a rational number can be expressed as a ratio of two integers a/b with b not equal to zero. In decimal form a rational number either terminates or repeats. An irrational number has decimal form that neither terminates nor repeats and it cannot be written as the ratio of two integers. Then we found that together rational and irrational numbers form real numbers. We found that if an integer is not a perfect square its square root is irrational.
Chapter 10 Summary and Review – We completed the review section where we practiced writing an equation of a line satisfying the given conditions using the slope-intercept form. Then we practiced writing an equation of a line that passes through a given point and is either parallel or perpendicular to the graph of a given equation. Next we practiced finding the midpoint of a line.
Assignment: Complete the Algebra 1 Review for Chapter 10 Quiz (Lessons 10-5 through 10-7)
10-6 Parallel and Perpendicular Lines – We reviewed the fact that if 2 lines have the same slope they are parallel and if the slopes are inverse reciprocals then the lines are perpendicular. We went over the critical thinking problem from Thursday’s homework. We learned that you can get the equation of the line in between the two parallel lines by finding the midpoint between the y- intercepts. Then you have the y-intercept of the line in between them and the slope has to be the same since they are all parallel. Next we moved on to Lesson 10-7 Midpoint of a Line Segment. We learned how to find the coordinates of the midpoint of a line segment in the coordinate plane given the coordinates of the endpoints. Then we learned how to find the other end point when you know one end point and the midpoint of a line segment. All of the homework was completed. Now we are waiting for the review for the test on chapter 10.
10-5 Writing Slope-Intercept Equations of Lines and 10-6 Parallel and Perpendicular Lines – We learned to write a linear equation in slope-intercept form given the slope of a line and the coordinates of a point on the line. Then we practiced writing a linear equation in slope-intercept form given the coordinates of two points on a line. Next we practiced writing an equation of a line that passes through a given point and is parallel or perpendicular to the graph of a given equation.
