Johnny Martinez Period 7th Pythagorean Theorem The Pythagorean Theorem also known as Pythagoras’s theorem is a relation in Euclidean geometry that are the tree sides of a right triangle. It’s the sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse. The equation use for it is A squared plus B squared equals C squared.The Theorem relates the lengths of the three sides of any right triangle. The theorem is named after the ancient Greek. There is evidence that indicates that Pythagorean Theorem was well- known to the mathematicians of the first Babylonian Dynasty (20th to 16th centuries BC) which would have been over a thousand years before Pythagoras was born. People say that Pythagoras discovered the theorem at least fifteen hundred years before Pythagoras was born. But no one really knows when it was founded or discovered. The Pythagorean Theorem was known long before Pythagoras but he might have been the…
At about twenty centuries ago there was an amazing discovery about right angled triangles: “In a right angled triangle the square of the hypotenuse is equal to the sum of squares of the other two sides.” It is called Pythagoras Theorem and can be written in one short equation: a²+b²=c² where c is the longest side of triangle and a and b are the other two sides. Pythagoras was born in the island of Samos in 570 BC in Greek in the eastern Agean. He was the son of Mnesarchus and his mother's name…
The theorem used to find the hypotenuse, adjacent, or opposite sides of a triangle is also used in Euclidian Geometry. “A” squared plus “B” squared equals “C” squared is the formula used in the theorem. For example, we are given two numbers in the sides of a triangle; if we are given the adjacent and opposite sides, and we must figure out the hypotenuse, we will be required to use the Pythagorean Theorem. The two numbers given are squared, and our third number, we obtain it from the sum of the…
Pythagoras was the ancient Greek philosopher and mathematician who lived in the sixth century B.C. In mathematics, the Pythagorean theorem is known as a fundamental relation in Euclidean geometry among the three sides of a right triangle. This theorem was named after him. For example, a right triangle is a triangle with a right angle; square corners adjacent sides also called square corners of the triangle beside it; hypotenuse is the side opposite the right angle. In the figure below, a and b…
call this point “B”. Vanessa will now turn 90 degrees to the right and will walk 2x+4 paces east until she is at point “C”. We have now acquired a line segment which we will call AB which is basically the line from A to B, the line segment from B to C is considered BC. However, the lines AB and BC intersect to form a perpendicular angel, and we will use line AC as Ahmed’s route. The end state of the line segments if one was to draw them out would equal a triangle. With the face that Vanessa had…
THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It…
This math challenge was easy to approach, because I realized that the lines O1O, O1O2, and O2O1, form a triangle, I realized that if that triangle was a right triangle I could find the distance between O1, and O. To prove that triangle OO1O2 is a right triangle I used the radii of O1, I realized that the sides of triangle PO1Q, O1P, and O1Q, are radii, and therefore they are equal. Since they are equal, the triangle PO1Q, is an isosceles triangle. In an isosceles triangle the base angles are…
If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…
The Van Hiele Theory applies to the article “Freedom Quilts and the Underground Railroad.” The three level of Van Hiele are used in the Freedom Quilt Activity. These three levels are recognizing figures by their appearance, recognizing/analyzing figures by their properties or components, and forming abstract definitions and classifying figures by their elaborating on their interrelationships. Students will be scaffolding as they are analyzing the shapes. At the second part of the activity, the…
However, by the end of the week/unit, the students will receive a summative assessment to demonstrate their understanding of using the Pythagorean Theorem to identify the missing leg or hypotenuse of a right triangle. Procedure: Before the lesson (Do Now): To help the students be successful with using the Pythagorean Theorem, the students will review what it means if a number is squared, square roots, and solving expressions with single digit exponents. To ensure that the students understood…