These lessons will involve the students in investigating and understanding:
• Theorem 16: For a triangle, the product of the base and height does not depend on the choice of base.
Area of a triangle (conventional method) - Math Open Reference
Khan
video (for fun) Triangle area proofs not needed for LCHL
• Definition 38: The area of a triangle is half the base multiplied by the height.
Khan
• Theorem 17: A diagonal bisects the area of a parallelogram.
Parallelogram - math word definition - Math Open Reference
Theorem 17 - A Diagonal Bisects the Area of a Parallelogram - GeoGebraTube
• Theorem 18: The area of a parallelogram is the base multiplied by the height.
GeoGebratube Theorem 18 - Area of a Parallelogram
Suggested class activities
Students might engage in the following activities:
In the case of each of these types of triangles: equilateral, isosceles, right-angled and obtuse-angled:
draw three diagrams for each type of triangle showing each side as a base and the corresponding perpendicular height.
Students investigate the validity of the following statement and its converse: “Congruent triangles have equal areas”.