Parallel lines, Transversals, and Angles
... Just as right triangles are ubiquitous, parallel lines, and studies of their properties, are found all over the world. While I am quite certain that perpendicularity is a result of direct, tangible human experience, I am not clear on the genesis of parallelism. One of my colleagues has suggested flo ...
... Just as right triangles are ubiquitous, parallel lines, and studies of their properties, are found all over the world. While I am quite certain that perpendicularity is a result of direct, tangible human experience, I am not clear on the genesis of parallelism. One of my colleagues has suggested flo ...
In the four problems that follow, use your ruler and/or protractor to
... 25. A regular hexagonal mirror frame is to be built from strips of 2-inch-wide pine lumber. Look closely at the diagram below. At what angles a and b should the frame pieces be cut? ...
... 25. A regular hexagonal mirror frame is to be built from strips of 2-inch-wide pine lumber. Look closely at the diagram below. At what angles a and b should the frame pieces be cut? ...
base angles
... The parallel sides of a trapezoid are its bases. The nonparallel sides are its legs. Two angles that share a vase of a trapezoid are base ...
... The parallel sides of a trapezoid are its bases. The nonparallel sides are its legs. Two angles that share a vase of a trapezoid are base ...
Similar Polygons
... similar, the corresponding angles are congruent and the corresponding sides are proportional. If two polygons are similar, the ratios of the lengths of corresponding side are equal. The ratio is called the scale factor. ...
... similar, the corresponding angles are congruent and the corresponding sides are proportional. If two polygons are similar, the ratios of the lengths of corresponding side are equal. The ratio is called the scale factor. ...
Section 2.4 Notes: Congruent Supplements and Complements
... Name: ____________________________________________ ...
... Name: ____________________________________________ ...
Review of Functions and Transformations
... 8. Does this table as a whole have a constant or variable rate of change? --------------------------------------------------------------------------------------------------------------------Use the equation for questions 9-10. 9. What are the third, forth, and fifth terms? 10. What is the domain and ...
... 8. Does this table as a whole have a constant or variable rate of change? --------------------------------------------------------------------------------------------------------------------Use the equation for questions 9-10. 9. What are the third, forth, and fifth terms? 10. What is the domain and ...
Constructing Congruent Triangles
... Make congruent measuring arcs from both endpoints of the original side and both endpoints of the image side. (four total, with the same radius) Copy the span of one original angle (from one endpoint of the side) to one measuring arc on the image. Complete this angle by drawing the side. Mark the con ...
... Make congruent measuring arcs from both endpoints of the original side and both endpoints of the image side. (four total, with the same radius) Copy the span of one original angle (from one endpoint of the side) to one measuring arc on the image. Complete this angle by drawing the side. Mark the con ...
8.2 Similarity
... After studying this section, you will be able to use several methods to prove triangles are similar. ...
... After studying this section, you will be able to use several methods to prove triangles are similar. ...
Trigonometric functions
In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component). More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles (often right triangles). In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics. A common use in elementary physics is resolving a vector into Cartesian coordinates. The sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations through the year.In modern usage, there are six basic trigonometric functions, tabulated here with equations that relate them to one another. Especially with the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically, or by other means, and then derive these relations.