1-1 Vertical Angles Theorem Vertical angles are congruent. Theorem 1-2 Congruent Supplements Theorem If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent. Theorem 1-3 Congruent Complements Theorem If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent. Theorem 2-1 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. Theorem 2-2 Exterior Angle Theorem The
There are multiple methods that can be used to find the sides and angles of a triangle, such as Special Right Triangles (30, 60, 90 and 45, 45, 90), SOHCAHTOA, and the Law of Sines and Cosines. These methods are very helpful. I will explain how to use all three of them with examples at the end. The first example, Special Right Triangles, is used only with right triangles. To use this method, you need to have angle measures of 30, 60, and 90, or 45, 45, and 90. There is a "stencil" that goes with
Angle of Geese and Other Poems MOMADAY had been writing poetry since his college days at University of New Mexico, and this volume incorporates many of his earlier efforts. Momaday admired the poetry of Hart Crane as an undergraduate, and early poems like "Los Alamos" show Crane's influence. Under the tutelage of Yvor Winters at Stanford Momaday developed an ability to provide clear, precise details and images in his verse. As a graduate student at Stanford, Momaday absorbed the influence
The Relationship between the Angle of Elevation of a Ramp and the Speed of a Ball Introduction In this piece of coursework I'm going to investigate and measure the speed of the ball rolling down a ramp. From the data that I'm going to collect I'm going to be able to work out the Gravitational potential energy when changing the height, the friction force acting on the ball whilst it rolling down, and finally the kinetic energy exerted by the ball. Planning Fair Testing Before
Investigating How the Size of a Shadow Depends on the Angle at Which the Light Hits the Object Introduction ============ The aim of the project is to see which factors affect the size of a shadow and then to look more closely at one of the factors to see how exactly it varies the size of a shadow. Variables that may affect the size of the shadow ================================================ Although, I will investigate how one factor affects the size of a shadow, there
Investigating the Relationship Between the Lengths, Perimeter and Area of a Right Angle Triangle Coursework Aim To investigate the relationships between the lengths, perimeter and area of a right angle triangle. Pythagoras Theorem is a² + b² = c². 'a' being the shortest side, 'b' being the middle side and 'c' being the longest side of a right angled triangle. So the (smallest number)² + (middle number)² = (largest number)² The number 3, 4 and 5 satisfy this condition 3²
an object in motion is affected by the angle of an inclined ramp on which it travels. Research Question How does the angle of inclination (º) of a ramp affect the velocity (m/s) of an object in motion, if calculated using the formula [V= (2s/t) –u]? Hypothesis The prediction for this experiment is that the final velocity of an object in motion will be affected according to the angle of inclination of the ramp. The higher the inclination or greater the angle, the greater the final velocity, however
Applications of Trignometry Trigonometry is the branch of mathematics that is based on the study of triangles. This study helps defining the relations between the different angle measures of a triangle with the lengths of their sides. Trigonometry functions such as sine, cosine, and tangent, and their reciprocals are used to find the unknown parts of a triangle. Laws of sines and cosines are the most common applications of trigonometry that we have used in our pre-calculus class. Historically. Trigonometry
collect is: the height and centre of mass for each block and the angle at which they fall. I will need to use five regular blocks, the board I will use to raise the blocks must be flat and level and likewise so must the surface I am working on. I will use my scientific knowledge of center of mass to predict at what point the block will fall over. I will raise the board until the block falls over and then I will record the angle at which it falls. I will vary the height of the block each time
When researching the math behind sports, I found that there are a multitude of formulas that go behind the simple actions in sports such as basketball and baseball. Basketball is a game played between two teams of five players in which goals are scored by throwing a ball through a netted hoop fixed above each end of the court. Baseball is a ball game played between two teams of nine on a field with a diamond-shaped circuit of four bases. To be successful in these sports, one must make their baskets
and Rotation * Angles Once I had my ideas, I asked the teachers in the department what they would prefer the resource to be. Most thought that reflection and rotation was easier to teach than the others, and that more resources were available to them for that area of mathematics. The general consensus was that either of the other three was fine. So I have chosen to base my resource on angles with some properties of quadrilateral and triangles as supplement to the angles work. A factor
grooved holder with their polarization axes lined up, and a bright red light emitting diode (LED) was placed on one side, and a light sensor was placed on the other side. Light intensity was measured as a function of the plastic rotating polarizer angle from 0 to 180 degrees. Science Workshop was used to measure the intensity for every 5-degree rotation (Fig 1). Method 2: The mineral calcite exhibits birefringence (double refraction), and therefore has two different values for its index of refraction
clear the net and then land within the boundaries of the court. In modern volleyball the game has progressed to more of a vertical game, with jump serving. The advantages that jump serving gives have to do with the physics of projectile motion. The angle in which the server’s initial velocity has to start from is smaller, because as the height increases the slope of the parabola in the motion of the ball decreases. As the height of contact increases the path that the ball follows becomes line like
Trigonometry Trigonometry uses the fact that ratios of pairs of sides of triangles are functions of the angles. The basis for mensuration of triangles is the right- angled triangle. The term trigonometry means literally the measurement of triangles. Trigonometry is a branch of mathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and
laws of physics, such as the law of gravitation. Sometimes, we might wonder how kinetics might apply in the Pokémon world: Team Rocket is sent blasting off again! They are struck by Pikachu's lightning bolt and are initially thrown at a 60 degree angle with an unknown speed. We do however know that they “land” in a body of water 114.5 meters away (assumed to be leveled) 6.363 seconds later. What is the speed that Team Rocket are thrown and what was their maximum height? Assume no air resistance or
What is a hydrofoil? A hydrofoil is a watercraft that is supported on ski-like pontoons while in motion, with the bulk of the hull remaining entirely above the water (Encarta Encyclopedia 2002). Hydrofoils were first seen about in 1869. Emmanuel Denis Farcot was issued a patent on a boat that he had developed to go faster through the water because of less resistance. If you look at his design, he was using many little foils along the side of his boat to lift it out of the water in order to reduce
Tompkins examines the conflicts between the English settlers and the American Indians. After examining several primary sources, Tompkins found that different history books have different perspectives. It wasn’t that the history books took different angles that was troubling, but the viewpoints contradicted one another. People who experience the same event told it through their reality. This becomes a problem when a person who didn’t experience the effect wants to know what happened. Tompkins said,
parts of the world to see places most people will not, or perhaps some places that most people do not even know exist. I am going to make an attempt to do some extreme activities in an attempt to experience life from another angle. Again, an angle most people just do not see, an angle hopefully a little too far off a tangent the average person. To experience life and take advantage of it, one needs to make promises to oneself. A person may wonder, “How am I supposed to do this? How can I possibly accomplish
well as figure out the best angle to send the ball where it needs to be. Throwing a deep ball is all about using the right angle with the right amount of force. I want to find out at which angle is the best to throw the ball the farthest. The angles I will test will be a low angle at 15˚, a medium angle at 45˚, and a high angle at 75˚. The force throwing the ball will be the same and the tight spiral will be assumed constant, so the only factor changing will be the angle at which the ball is being
apparent positions of objects produced by a shift in the position of the observer” (Columbia Electronic Encyclopedia 1). Parallax is commonly used to measure distances between celestial bodies, such as planets and stars. Parallax is measured using angles that are much smaller than a degree. Arcminutes are one sixtieth of a degree and arcseconds are one sixtieth of an arminute. One example of the infinitesimal size of an arcsecond could be the width of a dime from a point of view two kilometers away