Points to note:
- We cannot assume that a line is straight or that there is a right angle unless they provide us that information.
- We can only conclude that lines are parallel if they draw arrows on the line indicating they are parallel.
- Constructing is NOT the same as drawing or sketching.
Angle BXF = Angle DYF (Corr. angles; AB//CD) [corresponding angles]
Angle AXF + Angle CYE = 180° (int. angles; AB//CD) [interior angles]
Angle DYF = Angle CYE (vert. opp. angles) [vertically opposite angles]
Constructing a perpendicular bisector:
- Use a compass
- Cut above
- Cut below
- Equal distance from both points
Every point along the constructed line has an equal distance to the two points at the ends.
The triangle formed between a point on the constructed line and the points on the original given line would be an isosceles triangle.
To find the area of this triangle, use the length from where the constructed line cuts the base of the triangle to the point on the constructed line as the height. The base would be the length from one point of the original given line to another point on the same line. The area would be the product of both these lengths divided by half.