6.3 - Conditions for Parallelograms
- Author:
- Shawn Remy
In this investigation, you will determine what conditions a quadrilateral must meet in order to form a parallelogram.
Congruent Opposite Angles
In the quadrilateral below, the opposite angles are congruent. Move the green points to form several different quadrilaterals.
Will a quadrilateral with congruent opposite angles always form a parallelogram? Use the Geogebra tools to test your answer.
Congruent Opposite Sides
In the quadrilateral below, the opposite sides are congruent. Move the green points to form several different quadrilaterals.
Will a quadrilateral with congruent opposite sides always form a parallelogram? Use the Geogebra tools to test your answer.
Diagonals that Bisect Each Other
The segments below bisect each other. Use the tools to create quadrilateral AEBD. Move the green points to change the shape of your quadrilateral.
Will a quadrilateral with bisecting diagonals always form a parallelogram? Use the Geogebra tools to test your answer.
Congruent Diagonals
The segments below are congruent. Use the tools to create quadrilateral ACBD. Move the green points or the red segment to change the shape of your quadrilateral.
Will a quadrilateral with congruent diagonals always form a parallelogram? Use the Geogebra tools to test your answer.
Perpendicular Diagonals
The segments below are perpendicular. Use the tools to create quadrilateral ADBE. Move the green points to change the shape of your quadrilateral.
Will a quadrilateral with perpendicular diagonals always form a parallelogram? Use the Geogebra tools to test your answer.
One Pair of Opposite Sides that are both Parallel and Congruent
The segments below are both parallel and congruent. Use the tools to create quadrilateral ADFC. Move the green points to change the shape of your quadrilateral.
Will a quadrilateral with one pair of opposite sides that are both parallel and congruent always form a parallelogram? Use the Geogebra tools to test your answer.
Summarize Your Findings
1. Four of the conditions above should have resulted in a parallelogram always being formed.
In your notes, write down these conditions in the following form:
If _____ of a quadrilateral are _____, then the quadrilateral is a parallelogram.
2. Next to each of the statements you write in your notes, mark the diagram to reflect the information in the blue part of your statement.
3. Complete the problems in the notes.