Students explore a series of dynamic images and make conjectures about angles, including those formed with the diagonals, in a Rhombus, Kite and Trapezium. The extension task includes a simple proof.
ACMMG202: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning.
Corresponding, alternate, supplementary, complimentary, rhombus, kite, trapezium, parallelogram, congruent, transversal.
About the Lesson
Students are presented with a dynamic rhombus where the angles change as the shape is manipulated. Students record measurements and make conjectures about the interior angles. The diagonals are then included and results similarly recorded and reported. This process is repeated for a kite and trapezium. The extension task [ACMMG243] requires students to prove that opposite sides of a parallelogram are congruent using the definition of a parallelogram “a quadrilateral with two pairs of parallel sides.”