LINES AND ANGLES- ESSENTIAL POINTS
- A line-segment has two end points.
- A ray has only one end point (its vertex).
- A line has no end points on either side.
- An angle is formed when two lines (or rays or line-segments) meet.
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Pairs of Angles Condition Two complementary angles Measures add up to 90° Two supplementary angles Measures add up to 180° Two adjacent angles Have a common vertex and a common arm but no common interior. Linear pair Adjacent and supplementary
- When two lines a and b intersect; the point of their meet is called the point of intersection.
- When 2 lines do not meet at any point however far we extend them, we call these lines as parallel lines.
- Line: A line is perfectly straight and extends forever in both directions.
- Line segment: A line segment is the part of a line between two points.
- Ray: A ray is part of a line that starts at one point and extends forever in one direction.
- Intersecting lines: Two or more lines that have one point in common.
- Transversal: A line intersects two or more lines that lie in the same plane in distinct points.
- Parallel lines: Two lines on a plane that never meet. They are always the same distance apart.
- Complementary Angles: Two angles that add to 90°.
- Supplementary Angles: Two angles that add to 180°.
- Adjacent Angles: Two angles have a common vertex and a common arm but no common interior points.
- Linear pairs: A pair of adjacent angles whose non-common sides are opposite rays.
- Vertically Opposite Angles: Two angles formed by intersection of two lines that have common arm.
- Angles made by Transversal: When two lines are intersecting by a transversal, eight angles are formed.
- Transversal of Parallel Lines: If two parallel lines are intersected by a transversal, then each pair of:
- Corresponding angles are congruent.
- Alternate interior angles are congruent.
- Alternate exterior angles are congruent.
- If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent to 90° angles.
- Sum of any 2 sides of triangle is greater than its third side.
- In right angled triangle, hypotenuse is the longest side.
- Sum of angles of triangle is 180 degree.
- A, B, C are collinear if AB + BC = AC.
