Summary Math Grade 12 Metacog Euclidean IEB

Euclidea Geometr
Grad 12 Note

Introducing triangles into circles

Similar polygons


● Polygons are similar if the corresponding angles are equal
● The sides of similar polygons are in proportion


Example:

, Proportionality (Areas of Triangles)


1. The areas of triangles with equal altitudes are in the same proportion
as the lengths of their bases
- Area ABC : Area DFE
- = AB : DF




2. Triangles on the same base or equal bases and between the same
parallel lines are equal in area
- Area ABC = Area ACD
- Same hight, same bases, thus, area is the same




3. Triangles with equal areas on the same side of the base lie between
parallel lines
- If ABC = Area of PEF
- Therefore you have parallel lines