The following geometrical
constructions are relevant to the section of the course on Plane Figures.


1. Triangles on the same base and between parallel lines are equal in area  2. To divide the quadrilateral ABCD into two equal areas by drawing a straight line from point B. 


3. The angle at the centre is twice the angle at the circumference  4. The angle in a semicircle is always 90º. 


5.
"Mean Proportional".
AB x BC = (BD)² (Conversion of a rectangle into a square of equal area) 
6.
If a tangent and a secant are drawn to a circle from an outside point then
……….
PA x PB = (PC)² 


7. In a "Cyclic Quadrilateral" the sum of the opposite angles is 180º(All four angles add to 360º)  8. The angle between a tangent and a chord equals the angle in the alternate segment. 


9.
To draw a triangle ABC given the base AB, base angle Ø and perimeter
P.
A and B are focal points. 
10.
To draw a triangle ABC given the base AB, base angle Ø and perimeter
P.
Bisect BD to locate C. 


11.
To draw a triangle ABC given the base AB, base angle Ø and perimeter
P.AR = (P ÷ 2)
AS = (P ÷ 2) BC is tangential to circle shown. 
12.
"Spiral Similarity"
Loci for B and C are linear. 