![Points, Lines, Planes, and Angles](http://s1.studyres.com/store/data/000499146_1-d5546144ff9aaad938909cad14b68714-300x300.png)
Slide 1
... If one side of a triangle is longer than another side, then the angle opposite the larger side is larger than the angle opposite the shorter side. If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. GH ...
... If one side of a triangle is longer than another side, then the angle opposite the larger side is larger than the angle opposite the shorter side. If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. GH ...
LTM 21 Text FINAL
... The above result for a cyclic hexagon with equal angles naturally leads to the general theorem as discussed LQ'H9LOOLHUVD WKDW´,IDF\FOLFQ-gon has all angles equal, then the two sets of alternate sides are HTXDOµDQGZKHUHF\FOLFQ-gons with all angles equal have been called semi-regu ...
... The above result for a cyclic hexagon with equal angles naturally leads to the general theorem as discussed LQ'H9LOOLHUVD WKDW´,IDF\FOLFQ-gon has all angles equal, then the two sets of alternate sides are HTXDOµDQGZKHUHF\FOLFQ-gons with all angles equal have been called semi-regu ...
Congruent Triangles
... - SSS (side side side) All three corresponding sides are equal in length. See Triangle Congruence (side side side). SAS (side angle side) A pair of corresponding sides and the included angle are equal. See Triangle Congruence (side angle side). ASA (angle side angle) A pair of corresponding an ...
... - SSS (side side side) All three corresponding sides are equal in length. See Triangle Congruence (side side side). SAS (side angle side) A pair of corresponding sides and the included angle are equal. See Triangle Congruence (side angle side). ASA (angle side angle) A pair of corresponding an ...
Lesson 7: Solve for Unknown Angles—Transversals
... the class progresses; check to see whether facts from Lesson 6 are fluent. Encourage students to draw in all necessary lines and congruent angle markings to help assess each diagram. The Problem Set should be assigned in the last few minutes of class. ...
... the class progresses; check to see whether facts from Lesson 6 are fluent. Encourage students to draw in all necessary lines and congruent angle markings to help assess each diagram. The Problem Set should be assigned in the last few minutes of class. ...
Unit 5 Similarity and Triangles
... 1. How can you determine whether two figures are similar using similarity transformations, angle measures, and side lengths? 2. What is the AA Similarity theorem and why does it sufficiently determine whether two triangles are similar or not? 3. How can you prove that a line parallel to one side of ...
... 1. How can you determine whether two figures are similar using similarity transformations, angle measures, and side lengths? 2. What is the AA Similarity theorem and why does it sufficiently determine whether two triangles are similar or not? 3. How can you prove that a line parallel to one side of ...
Unit 7 – Polygons and Circles Diagonals of a Polygon
... Participants will now investigate the exterior angles of a polygon. It is often difficult for students to understand intuitively that this sum does not depend on the number of sides of the polygon. Participants may use the polygons that they have already constructed to study exterior angles for the ...
... Participants will now investigate the exterior angles of a polygon. It is often difficult for students to understand intuitively that this sum does not depend on the number of sides of the polygon. Participants may use the polygons that they have already constructed to study exterior angles for the ...
Chapter_4_Vector_Add..
... 1.6.1. A and B are vectors. Vector A is directed due west and vector B is directed due north. Which of the following choices correctly indicates the directions of vectors A and B? a) A is directed due west and B is directed due north b) A is directed due west and B is directed due south c) A ...
... 1.6.1. A and B are vectors. Vector A is directed due west and vector B is directed due north. Which of the following choices correctly indicates the directions of vectors A and B? a) A is directed due west and B is directed due north b) A is directed due west and B is directed due south c) A ...
New Class Notes in PDF Format
... 1.2.1. Quantifiers. One frequently makes statements in mathematics which assert that all the elements in some set have a certain property, or that there exists at least one element in the set with a certain property. For example: • For every real number x, one has x2 ≥ 0. • For all lines L and M, if ...
... 1.2.1. Quantifiers. One frequently makes statements in mathematics which assert that all the elements in some set have a certain property, or that there exists at least one element in the set with a certain property. For example: • For every real number x, one has x2 ≥ 0. • For all lines L and M, if ...
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.