Lines, Rays & Angles

A point is one exact spot on the paper, drawn as a small dot with a label like point A. A line runs straight forever in both directions, so it gets an arrow on each end. A line segment stops at two endpoints, so it has no arrows. A ray starts at one endpoint and runs forever in one direction, so it gets one arrow.

Drawing method: use a ruler for every straight part. Mark each point as a dot before you draw. For a segment, lay the ruler between two points and stop at both. For a ray, start at the endpoint and draw one straight path, then add an arrow. For a line, draw straight and add arrows on both ends. Check each part with the ruler edge: it must lie flat and straight.

Arrows mark the parts that go on forever. A line has two, a ray has one, a segment has none.

Parallel lines are straight paths in the same flat plane that never meet, even stretched forever. The gap between them stays the same all along. Perpendicular lines cross at a square corner, a right angle, and make four right angles at the crossing. Two short segments that do not touch are not automatically parallel: extend both paths and check the gap stays fixed.

Squared-paper construction: on squared paper, grid rows and grid columns are perpendicular. Draw a first line along a grid row. Mark point P where a grid column crosses another row. The parallel through P follows that row. The perpendicular through P follows its column and extends across the first line. Both get arrowheads, since ideal lines go on forever.

An angle is the opening between two rays that meet at one shared endpoint. Real segments and clock hands stand for the ray directions. A right angle is a quarter turn, 90 degrees. A straight angle is a half turn, 180 degrees. An acute angle has a positive opening smaller than 90 degrees. An obtuse angle is greater than 90 degrees and less than 180 degrees. A zero opening is not acute.

Marking rule: draw a small square box at a right angle. Use a small arc for acute and obtuse angles. The arc radius does not measure the opening. A trapezoid is a closed shape with 4 straight sides and, under this lesson's convention, exactly one pair of parallel sides. Some books use at least one pair, and both are valid.