A plane convex quadrilateral is a parallelogram, if and only if, it has[b] opposite parallel sides[/b]. In the following figure AB//CD (AB is parallel to CD) and AC//BD (AC is parallel to BD).
Opposite congruent angles.[br]
Change points A, B or C. What do you notice?
[justify]Research and prove the argument of following property: "Every convex quadrilateral that has congruent opposite angles is a parallelogram" (Note: consider the following figure and remember that the sum of the internal angles of the quadrilateral is 360º).[/justify][img]https://cdn.geogebra.org/material/R4NBmqjPu54RHp0sxt3aBNPrqhDkGPj8/material-GcEtXXUp.png[/img][br][br]
Congruent opposite sides.
Change points A, B or C. What do you notice?
[justify]Research and prove the argument of following property: "Every convex quadrilateral that has opposing congruent sides is a parallelogram" (Note: Draw a diagonal and use triangle congruence). [/justify]
Change vertices A, B or C. What do you notice?
[justify]Research and prove the argument of following property: "Every convex quadrilateral is a paralellogram, when their diagonals intersect at midpoints" (note: use the following figure as reference).[/justify][img]https://cdn.geogebra.org/material/OQ66wt5olzhmKFLb8LexaTYMQqcAK2lh/material-nD5XjzHR.png[/img][br]
Move points A, B or C of the previous figure. What can you notice?[br][br]
[justify]Research and prove the argument of following property: "Every convex quadrilateral is a parallelogram, when they have two parallel sides and congruent sides " (note: use the following figure as a reference).[/justify][center][img]https://cdn.geogebra.org/material/lvMF8DxzEAavOrpIU5UFhv55eGBpDRFA/material-gRfN6qAc.png[/img][/center][br]