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How does sas theorem answer?
The SAS theorem is used to prove that two triangles are congruent. If the triangles have a side-angle-side that are congruent (it must be in that order), then the two triangles can be proved congruent. Using this theorem can in the future help prove corresponding parts are congruent among other things.
What was Pythagoras great for?
Pythagoras is great for all the things he did. Including: Making Pythagoras' Theorem and even more.
How do you calculate the length of a cord of a circle?
-- Take the information you're given, such as, for example, the circle's radius or diameter, and the distance from the center of the circle to the chord's midpoint. -- Jot down a few things you know about circles and right triangles, such as the relationship between the radius, diameter, and circumference of a circle, and the Pythagorean Theorem. -- Use what you're given, combined with what you know from your studies and your general knowledge, to calculate what is required.
One way to simplify things in geometry is to divide what you see into groups of objects that share a property or?
characteristic. By classifying shapes based on attributes such as sides, angles, or symmetry, you can better understand their relationships and properties. For instance, grouping all triangles together allows for easier analysis of their properties, such as the Pythagorean theorem for right triangles. This method of categorization streamlines problem-solving and enhances comprehension of geometric concepts.
Why do you use pythagorean theorem?
The Pythagorean theorem is used to describe the relationship of the hypotenuse (the longest side) of a right triangle to its other two sides, where a right triangle is described as a three-sided shape where the angle between two of its sides is square, or 90 degrees. We can use the theorem, for example, to determine the shortest linear distance between one point and another, as long as we know how far to it is away in two directions. To wit: If I know that an apple is 4 feet to the right of me and 3 feet in front of me, the shortest distance to the apple is directly along the hypotenuse of the triangle formed by joining those two "legs" of the trip. Since the question does not venture into how the theorem is calculated, I will simply leave off with some related comments: 1) It is important to note that there are other theorems for solving triangles. Triangulation, perhaps best attributed in today's age to locating a cell phone making an emergency call, might use the Law of Sines to find the phone. Indeed, the Law of Cosines reduces to the pythagorean theorum when it is used on a right triangle. 2) It is shortsighted to assume that the theorem is only useful in 2-dimensional geometry. It is in fact extremely important in 3D, not only because our games' virtual environments are drawn in triangles (where many video cards rate how many triangles can be drawn per unit of time), but also because engineering depends on a basic understanding of how much force pushes in two directions, which leads to how much it pushes in a third direction. While this is a basic description because we're actually dealing with three dimensions, this theorem is fundamental to such calculations. 3) Related to engineering, it is also possible to determine the heights of things that would be difficult to measure otherwise. It's not practical to drill a hole through the peak of a mountain to its base in order to determine its height by dropping a tape measure down the hole. It is practical to take measurements from some point at the base to a locater at the the top (giving the hypotenuse), determine the horizontal distance from the centerline of the mountain to your position (giving another leg), and rearranging the theorem--using basic rules of algebra--to determine the vertical distance to the top. 4) More advanced math utilize properties of this formula to continue to more interesting problems, but that is outside of the scope of this question. The short answer is: our scientists, engineers, designers, and people of all professions use the theorem to answer some very basic questions about measurements made in their respective fields.
What are the uses of the Pythagorean theorem?
The Pythagorean theorem can be used to find distances between two points on a graph. It can also be used to measure unknown heights of things, like a television. In baseball, one could use the Pythagorean theorem to figure out how far a second baseman has to throw in order to get an out at home plate.
How is the pythagorean theorem used in modern day times?
The Pythagorean theorem is used for many things today. For example, it can be used for building. Putting in flooring deals with squares and triangles using the Pythagorean Theorem. Some builders use this formula, because they can find the missing sides. The Pythagorean theorem plays an important role in mathematics, too. For example: -It is the basis of trigonometry -using the theorems arithmetic form, it connects algebra and geometry. -It is linked to fractal geometry His theorem is not only important in 2-D geometry, but also in 3-D geometry. Video games environments are drawn in 3-D using all triangles. i got this information from a website called: [See below for the related link to this website]. This website tells you all about how the Pythagorean theorem is used in modern day.
How is Pythagorean theorem used today?
The theorem of Pythagoras is used in mathematics (primarily in trigonometry and geometry), physics (for a variety of things) and is also employed in architecture and design. it is also used to find any side of a right angle triangle
How many things did Ancient Greeks invented and discovered?
The Ancient Greeks discovered and invented tons of things- we don't have an exact number. They also invented things that weren't physical, tangible objects- philosophy, the Socratic Method, and the Pythagorean Theorem, for example.
How has the Pythagorean theorem helped mankind?
Amongst other things, it helped ancient builders measure out right angles. That is quite a useful trick when you are trying to build walls that are vertical - assuming you would like them to remain standing!
Who is Pythagoras and Euclid?
Pythagoras and Euclid are both mathematicians. Pythogoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides-that is, . Euclid is in charge of dicovering Pythagorean Triples, Euclidean geometry and more geometry realated things. Euclid also wrote a book called "Elements" in support of his math.
What does it mean to wear Pythagorean Spectacles?
This expression, as related to geometry, means that Cartesian workspace is analyzed in respect to the presence of right triangles, especially those believed to describe squared circles. As modern criticism of these hopeful geometers, "wearing Pythagorean Spectacles" alludes to the "proven" futility of this ancient geometry challenge. As related to philosophy, "wearing Pythagorean Spectacles" alludes to belief that all real things can be described in terms of mathematical constructs (albeit positional relationships of physical things can often be described in terms of geometric constructs).
What are 3 main discoveries of Pythagoras?
Pythagoras biggest impact on people today was the Pythagorean Theorem. Some other things he has influenced people with are the discovery that music notes could be used in mathematical problems, he devising the tetractys, and which is a triangular figure of four rows
What is the length of the diagonal of a 10 by 10 ft square?
To find the length of the diagonal of a square, we can use the Pythagorean theorem. In a square, the diagonal divides the square into two right-angled triangles. The Pythagorean theorem states that the square of the length of the diagonal is equal to the sum of the squares of the two sides. Therefore, for a 10 by 10 ft square, the length of the diagonal would be the square root of (10^2 + 10^2) which is √(100 + 100) = √200 = 10√2 feet.
How does sas theorem answer?
The SAS theorem is used to prove that two triangles are congruent. If the triangles have a side-angle-side that are congruent (it must be in that order), then the two triangles can be proved congruent. Using this theorem can in the future help prove corresponding parts are congruent among other things.
What was Pythagoras great for?
Pythagoras is great for all the things he did. Including: Making Pythagoras' Theorem and even more.
How do you calculate the length of a cord of a circle?
-- Take the information you're given, such as, for example, the circle's radius or diameter, and the distance from the center of the circle to the chord's midpoint. -- Jot down a few things you know about circles and right triangles, such as the relationship between the radius, diameter, and circumference of a circle, and the Pythagorean Theorem. -- Use what you're given, combined with what you know from your studies and your general knowledge, to calculate what is required.
