Non-Euclidean Geometries
... I-3. If two points lie in a plane, then any line containing those two points lies in that plane I-4. It two distinct planes met, their intersection is a line ...
... I-3. If two points lie in a plane, then any line containing those two points lies in that plane I-4. It two distinct planes met, their intersection is a line ...
Moore Catholic High School Math Department
... parallel lines - Two or more coplanar lines that do not intersect. parallelogram - A quadrilateral in which both pairs of opposite sides are parallel. pentagon - A polygon with 5 sides. perimeter - The sum of the lengths of all the sides of any polygon. perpendicular lines - Two lines that intersect ...
... parallel lines - Two or more coplanar lines that do not intersect. parallelogram - A quadrilateral in which both pairs of opposite sides are parallel. pentagon - A polygon with 5 sides. perimeter - The sum of the lengths of all the sides of any polygon. perpendicular lines - Two lines that intersect ...
Definitions Synthetic Geometry- the study of description of points
... 78. Line Intersection Theorem- Two different lines intersect in at most one point 79. Parallel Lines- Two coplanar lines m and n are parallel lines, written m // n if and only if they have no points in common or they are identical 80. Linear Pair Theorem- If two angles form a linear pair then they a ...
... 78. Line Intersection Theorem- Two different lines intersect in at most one point 79. Parallel Lines- Two coplanar lines m and n are parallel lines, written m // n if and only if they have no points in common or they are identical 80. Linear Pair Theorem- If two angles form a linear pair then they a ...
3-D Figures
... Two Point Perspective – two types of parallel lines meet at vanishing points and one type is drawn parallel. To draw in two point perspective: 1. Draw horizon and 2 vanishing points. 2. Draw the front vertical edge of your figure. 3. Connect both ends of the edge to both vanishing points. Draw the ...
... Two Point Perspective – two types of parallel lines meet at vanishing points and one type is drawn parallel. To draw in two point perspective: 1. Draw horizon and 2 vanishing points. 2. Draw the front vertical edge of your figure. 3. Connect both ends of the edge to both vanishing points. Draw the ...
Name: Period: ______ Geometry Unit 3: Parallel and Perpendicular
... REVIEW: Answer always, sometimes, or never for each question. 1. A scalene triangle is regular. 2. A theorem is a proven conjecture. 3. Planes intersect in a point. 4. Space is an infinite number of points. 5. A line can be named using three points. 6. Two points are collinear. 7. Two lines w ...
... REVIEW: Answer always, sometimes, or never for each question. 1. A scalene triangle is regular. 2. A theorem is a proven conjecture. 3. Planes intersect in a point. 4. Space is an infinite number of points. 5. A line can be named using three points. 6. Two points are collinear. 7. Two lines w ...
Conic section
In mathematics, a conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2, and as a quadric of dimension 1. There are a number of other geometric definitions possible. One of the most useful, in that it involves only the plane, is that a non-circular conic consists of those points whose distances to some point, called a focus, and some line, called a directrix, are in a fixed ratio, called the eccentricity.Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section. The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas. In the focus-directrix definition of a conic the circle is a limiting case with eccentricity 0. In modern geometry certain degenerate cases, such as the union of two lines, are included as conics as well.The conic sections have been named and studied at least since 200 BC, when Apollonius of Perga undertook a systematic study of their properties.