Goal (in simple words)
We have a straight angle (a straight line). We will use a ruler and a compass to split it into two equal parts and then measure each part.
( ext{Straight angle} = 180^circ)
( ext{Half of }180^circ = dfrac{180^circ}{2})
(= 90^circ)
What you need
- Ruler (scale)
- Compass
- Pencil
- Protractor (to measure)
Before we start
Draw a straight line and mark the middle point as O. The angle at O on a straight line is a straight angle.
Construction Steps (easy & clear)
- Set the compass: Place the compass needle at point O. Open it to a medium width (not too small, not too large).
- Make two marks on the line: With the same opening, draw an arc that cuts the straight line at two points.
Call the left point A and the right point B.
- Arcs above the line: Without changing the compass width,
- Place the needle at A and draw a small arc above the line.
- Place the needle at B and draw another small arc above the line so that it crosses the first arc.
Mark the crossing point as P.
- Draw the bisector: Use the ruler to draw a straight line from O to P. This line OP is the bisector of the straight angle.
Why this works (very short idea)
The arcs from A and B are drawn with the same radius. Their crossing point P is the same distance from A and from B.
So line OP is exactly in the middle, making two equal angles.
(angle AOP = angle POB)
(angle AOB = 180^circ)
( herefore angle AOP = angle POB = dfrac{180^circ}{2} = 90^circ)
Measure each part
- Place the protractor’s center on O and align its base line with OA.
- Read the angle up to line OP. You should get 90°.
- Do the same from OB to OP. You should again get 90°.
Result
The straight angle is divided into two equal right angles.
( ext{Each part} = 90^circ)
Common mistakes to avoid
- Do not change the compass width between steps 2 and 3.
- Make sure the two small arcs above the line actually intersect.
- Use a sharp pencil for clean points and lines.