Suggested activities
Students might engage in the following activities which lead to an informal proof of theorem 9:
Draw a parallelogram ABCD which is not a rectangle or a rhombus
Draw in one diagonal BD
Mark in all the alternate angles – they should find 2 pairs
Establish that triangles ABD and BCD are congruent and explain their reasoning
Establish what this means about the opposite sides of parallelogram ABCD?
Make a deduction about the opposite angles of parallelogram ABCD?
The students might determine:
If the diagonal bisects the angles at the vertex
The sum of the four angles of parallelogram ABCD
The result if two adjacent angles of the parallelogram are added together
Students might engage in the following activities which lead to an informal proof of theorem 10: (In all instances they should be encouraged to explain their reasoning.)
Draw a parallelogram ABCD which is not a rectangle or a rhombus
Draw in the two diagonals AC and BD intersecting at E Page 44 of 104
Determine if the two diagonals equal in length. (Measure)
Mark in all the equal sides and angles in the triangles AED and BEC
Explain why triangles ADE and BEC are congruent (Give a reason.)
Possible further investigations:
The students might determine:
If the triangles AEB and DEC congruent
If the diagonals perpendicular
If the parallelogram contains 4 two pairs of congruent triangles
If the diagonals bisect the vertex angles of the parallelogram
The number of axes of symmetry the parallelogram has
If the parallelogram has a centre of symmetry and its location if it does exist
Students might engage in the following activities about a square, rhombus, parallelogram and rectangle: (In all instances they should be encouraged to explain their reasoning.)
Describe each of them in words.
Draw three examples of each in different orientations.
Determine which sides are equal in length
Determine the sum of the angles in each case
Determine which angles are equal
Determine the sum of two adjacent angles in each case
Establish if a diagonal bisect the angles it passes through
Establish if the diagonals are perpendicular
Determine if a diagonal divide it into two congruent triangles
Calculate the length of a diagonal given the length of its sides, where possible
Establish if the two diagonals equal in length
Determine if the diagonals divide the different shapes into 4 congruent triangles?
Establish if the diagonals bisect each other?
The students should determine the number of axes of symmetry each of the shapes has and which ones have a centre of symmetry
An interesting option would be to conduct the activities above on a KITE.