Parallelogram
DEFINITION
Parallelogram
Property 1
Analysis
Change points A, B or C. What do you notice?
ARGUMENT
Exercise 1
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).
Property 2
Analysis
Change points A, B or C. What do you notice?
Exercise 2:
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).
Diagonals of the Paralellogram
Analysis
Change vertices A, B or C. What do you notice?
Proof of the Property
EXERCISE 3
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).
Move points A, B or C.
Exercise 4
Move points A, B or C of the previous figure. What can you notice?
Exercise 5
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).