![Lecture 2 : Euclidean geometry](http://s1.studyres.com/store/data/000792679_1-7f6c8c0d8710b5a64b3e5c8321399f18-300x300.png)
Vocab - Wsfcs
... perpendicular: 2 lines, form right angles where they cross plane: points forming a flat, continuous surface point: exact location in space polygon: closed figure, 3 or more straight sides ray: part of line, 1 end point, forever extends other direction regular: polygon, all sides & all angles congrue ...
... perpendicular: 2 lines, form right angles where they cross plane: points forming a flat, continuous surface point: exact location in space polygon: closed figure, 3 or more straight sides ray: part of line, 1 end point, forever extends other direction regular: polygon, all sides & all angles congrue ...
Patty Paper Worksheet 1
... 1. Fold a line on a patty paper. Unfold. Fold a second line intersecting the first line. Unfold. 2. Notice there are four angles surrounding the intersection of the two lines. Label them a, b, c, and d so that you can refer to each by name. 3. Are any angles the same? Are all the angles different? ...
... 1. Fold a line on a patty paper. Unfold. Fold a second line intersecting the first line. Unfold. 2. Notice there are four angles surrounding the intersection of the two lines. Label them a, b, c, and d so that you can refer to each by name. 3. Are any angles the same? Are all the angles different? ...
Similar Figures
... What are similar polygons? Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional. ...
... What are similar polygons? Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional. ...
Sample Paper – 2009 Class – X Subject – Mathematics(09/IS/) M
... total time of 4hours 30 minutes. Find the speed of the stream. 27. Prove that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Making use of the above, prove the following. In fig, ABCD is a rhombus. Prove that 4AB2 = AC2 + BD2 28. A ...
... total time of 4hours 30 minutes. Find the speed of the stream. 27. Prove that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Making use of the above, prove the following. In fig, ABCD is a rhombus. Prove that 4AB2 = AC2 + BD2 28. A ...
4.6 Isosceles, Equilateral, and Right Triangles
... if it has at least two congruent sides. If it has exactly two congruent sides, then they are the legs of the triangle and the noncongruent side is the base. The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle. ...
... if it has at least two congruent sides. If it has exactly two congruent sides, then they are the legs of the triangle and the noncongruent side is the base. The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle. ...
Geometry 1: Intro to Geometry Introduction to Geometry
... G-CO.9 I can prove theorems about lines and angles. 15. Draw a diagram that fits the following criteria: Draw two lines and a transversal such that 1 and 2 are corresponding angles, 2 and 3 are vertical angles, and 3 and 4 are corresponding angles. What type of angle pair is 1 and 4 ...
... G-CO.9 I can prove theorems about lines and angles. 15. Draw a diagram that fits the following criteria: Draw two lines and a transversal such that 1 and 2 are corresponding angles, 2 and 3 are vertical angles, and 3 and 4 are corresponding angles. What type of angle pair is 1 and 4 ...
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.