CASA Math Study Sheet Standard 11: Measurement and Geometry
... o Vertical Angle: Angles opposite each other when two lines cross that are also equal. o Adjacent Angle: Two angles are adjacent when they have a common side and a common vertex (corner point) and don’t overlap. o Similarity: Figures that are the same shape, but not necessarily the same size. o Cong ...
... o Vertical Angle: Angles opposite each other when two lines cross that are also equal. o Adjacent Angle: Two angles are adjacent when they have a common side and a common vertex (corner point) and don’t overlap. o Similarity: Figures that are the same shape, but not necessarily the same size. o Cong ...
Chapter 4 - Congruent Triangles
... a. Ramon places a mirror on the ground 40.5ft from the base of a geyser. He walks backwards until he can see the top of the geyser in the middle of the mirror. At that point, Ramon’s eyes are 6ft above the ground and he is 7ft from the image in the mirror. Use similar triangles to find the height of ...
... a. Ramon places a mirror on the ground 40.5ft from the base of a geyser. He walks backwards until he can see the top of the geyser in the middle of the mirror. At that point, Ramon’s eyes are 6ft above the ground and he is 7ft from the image in the mirror. Use similar triangles to find the height of ...
Chapter 2 - Catawba County Schools
... • A plane contains at least three noncollinear points. • If two points lie in a plane, then the line containing them lies in the plane. • If two planes intersect, then their intersection is a line. • If there is a line and a point not on the line, then exactly one plane contains them. ...
... • A plane contains at least three noncollinear points. • If two points lie in a plane, then the line containing them lies in the plane. • If two planes intersect, then their intersection is a line. • If there is a line and a point not on the line, then exactly one plane contains them. ...
A Foundation for Geometry
... Dana: As long as they’re distinct, why not? Professor: What if the three points all lie on the same line? Ernest: You’d get a really flat triangle. Professor: Do you want to even call such a thing a triangle? Dana: [grudgingly] I guess not. Professor: Triangle 4ABC is AB ∪ BC ∪ AC, provided that A, ...
... Dana: As long as they’re distinct, why not? Professor: What if the three points all lie on the same line? Ernest: You’d get a really flat triangle. Professor: Do you want to even call such a thing a triangle? Dana: [grudgingly] I guess not. Professor: Triangle 4ABC is AB ∪ BC ∪ AC, provided that A, ...
Warm-Up Exercises
... Use transformations to show figures are not similar SOLUTION Corresponding sides in the pentagons 2 are proportional with a scale factor of 3 . ...
... Use transformations to show figures are not similar SOLUTION Corresponding sides in the pentagons 2 are proportional with a scale factor of 3 . ...
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.