These lessons will involve the students in investigating and understanding:
• Different quadrilaterals
Khan
• Properties of parallelograms
Khan video CA Geometry: Triangles and parallelograms
Parallelogram and its properties. (Coordinate Geometry)
• *Theorem 9: In a parallelogram, opposite sides are equal, and opposite angles are equal
Conversely, (1) if the opposite angles of a convex quadrilateral are equal, then it is a parallelogram;
(2) if the opposite sides of a convex quadrilateral are equal, then it is a parallelogram.
• Remark 1 Sometimes it happens that the converse of a true statement is false. For example, it is true that if a quadrilateral is a rhombus, then its diagonals are perpendicular. But it is not true that a quadrilateral whose diagonals are perpendicular is always a rhombus.
• Remark 2: The converse of Corollary 1 is false: it may happen that a diagonal divides a convex quadrilateral into two congruent triangles, even though the quadrilateral is not a parallelogram.
ProjectMaths Theorem 9
Parallelogram - math word definition - Math Open Reference
Khan
video Proof: Opposite sides of parallelogram congruent | Quadrilaterals ...
video Proof: Opposite angles of parallelogram congruent | Quadrilaterals ...
• Further properties of parallelograms
Interior angles of a parallelogram
• Use of the term “corollary
• Corollary 1: A diagonal divides a parallelogram into two congruent triangles
• Theorem 10: The diagonals of a parallelogram bisect each other.
Conversely, if the diagonals of a quadrilateral bisect one another, then the quadrilateral is a parallelogram.
Project Maths Theorem 10
Parallelogram diagonals bisect each other - Math Open Reference
Khan video Proof: Diagonals of a parallelogram bisect each other ...
• Construction 20: Parallelogram, given the length of the sides and the measure of the angles.
Project Maths Construction 20
Construction 20 - Parallelogram - YouTube
• The properties of different quadrilaterals
Khan