Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lie sphere geometry wikipedia , lookup
Perspective (graphical) wikipedia , lookup
History of trigonometry wikipedia , lookup
Cartesian coordinate system wikipedia , lookup
Möbius transformation wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Trigonometric functions wikipedia , lookup
Derivations of the Lorentz transformations wikipedia , lookup
Rational trigonometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Transformations in the Coordinate Plane Vocabulary Point • A point is an exact location. It has no size, only position. Line • is straight (no curves), • has no thickness, and • extends in both directions without end (infinitely). Perpendicular Line • Lines that are at right angles (90°) to each other. • Their slopes are negative reciprocals of each other Parallel Line • Two lines on a plane that never meet. They are always the same distance apart. Line Segment • In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its end points. Distance Along A Line • Also known as the distance between two points Ray • A line with a start point but no end point (it goes to infinity) Angle • The amount of turn between two straight lines that have a common end point (the vertex). • A shape, formed by two lines or rays diverging from a common point (the vertex). Right Angle • An angle which is equal to 90°, one quarter of a full revolution. Acute Angle • An angle less than 90° (90° is called a Right Angle) Obtuse Angle • An obtuse angle is one which is more than 90° but less than 180° In other words, it is between a right angle and a straight angle Straight Angle • An angle whose measure is 180. It is also a line. Reflex Angle • A Reflex Angle is one which is more than 180° but less than 360° Circle • A circle is a shape with all points the same distance from its center. A circle is named by its center. One-to-One A relationship wherein each point in a set of points is mapped to exactly one other point. Pre-image The original figure before undergoing a transformation. Image The new, resulting figure after a transformation Isometry A transformation in which the preimage and image are congruent. Transformations are called RIGID if every image is congruent to its preimage. Rigid transformations can also be referred to as an ISOMETRY. Every segment is congruent to its image. Which of the following are rigid transformations? (Isometry) Find the value of each variable, given that the transformation is an isometry. 72 10 6 x3 y 2 x 12, y 4 Congruent Figures are congruent if they have the same shape, size, lines, and angles. Similar Triangles Triangles are similar if they have the same shape but have different sizes.