Download SECTION 12.3 – PROPERTIES OF GEOMETRIC SHAPES: LINES

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.)