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Download SECTION 12.3 – PROPERTIES OF GEOMETRIC SHAPES: LINES
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Transcript
SECTION 12.3 – PROPERTIES OF GEOMETRIC SHAPES: LINES AND ANGLES PLANE: infinitely large flat surface LINE: extends infinitely in two directions COLLINEAR POINTS: points that lie on the same line. PARALLEL LINES: Two lines in the same plane are parallel if they do not intersect or are the same. SKEW LINES: Two lines that do not intersect and are not parallel. CONCURRENT LINES: Three or more lines that contain the same point. PROPERTIES OF POINTS AND LINES: • For each pair of points A and B (A 6= B) in the plane, there is a unique line AB containing them. • The distance between points A and B is the nonnegative difference of the real numbers a and b to which A and B correspond. The distance is written AB or BA. (a and b are called coordinates of A and B on AB). • If a point P is not on a line `, there is a unique line m, m 6= `, such that P is on m and m is parallel to `, written m k `. ANGLE: union of two line segments (or two rays) with a common endpoint, called a vertex. ADJACENT ANGLES: two angles that share a vertex, have a common side, but whose interiors do not intersect. CLASSIFICATION OF ANGLES ACCORDING TO MEASUREMENT: • acute angle: angle measuring less than 90◦ • right angle: angle measuring 90◦ • obtuse angle: angle measuring more than 90◦ but less than 180◦ • straight angle: angle measuring 180◦ • reflex angle: angle measuring more than 180◦ CLASSIFICATION OF TRIANGLES ACCORDING TO ANGLES: • right triangle: triangle with a right angle. • obtuse triangle: triangle with an obtuse angle. • acute triangle: triangle with all acute angles. • equiangular triangle: triangle with all angles the same measurement. IMPORTANT: The sum of the measures of the angles of a triangle is 180◦ . OTHER CLASSIFICATIONS OF ANGLES: 1. vertical angles: opposite angles formed by a pair of intersecting lines. (IMPORTANT: vertical angles have the same measurement) 2. Supplementary angles: two angles whose measures sum to 180◦ 3. Complementary angles: two angles whose measures sum to 90◦ ANGLES ASSOCIATED WITH PARALLEL LINES: • corresponding angles: have the same location relative to `, m and t. (IMPORTANT: ` k m if and only if corresponding angles formed by `, m, and t are congruent.) • alternate interior angles: nonadjacent angles formed by `, m, and t, the union of whose interiors contain the region between ` and m. (IMPORTANT: ` k m if and only if alternate interior angles formed by `, m and t are congruent.) • alternate exterior angles: (IMPORTANT: ` k m if and only if alternate exterior angles formed by `, m and t are congruent.) • interior angles on the same side of the transversal: interior angles whose interiors are the same. (IMPORTANT: ` k m if and only if the interior angles on the same side of the transversal are supplementary.)