Summary Triangle Geometry (Proportionality) - Mathematics Grade 12 (IEB)

Triangle Geometry - Proportionality
Important concepts:

1. Area of a triangle

1. a. The height or altitude of a triangle is always relative to the chosen base.




1. In all cases, the area of the triangles can be calculated by the formula:
1
1. Area ∆ ABC = 2 x base x height

1. b. Two triangles which share a common vertex have a common height.




1. c. Triangles with equal or common bases lying between parallel lines have the same area.




Area ∆ ABC = Area ∆ DBC Area ∆ EFH = Area ∆ HGE

, 2. Ratios
21 cm
Example:
A B
4 parts C 3 parts
AC : CB = 4 : 3
4 + 3 ≠ 21

Let each part = k
∴ 4k + 3k = 21
k = 3 cm

AC = 12 cm
CB = 9 cm



3. Cross multiplication techniques


𝑎 𝑐
If = , then:
𝑏 𝑑
𝑏 𝑑
𝑎
=𝑐 Invert both fractions


𝑎 𝑏
𝑐
=𝑑 Interchange the one fractions denominator with the others numerator


𝑑 𝑐
𝑏
=𝑎 Interchange the one fractions denominator with the others numerator


ad = bc Multiply both denominators out

𝑎𝑑
𝑏
=c Multiply the one denominator out


𝑏𝑐
𝑑
=a Multiply the one denominator out