Def 1: A parallelogram is a quadrilateral with two pairs of parallel sides. Attention: big mistake: do not mix up parallelograms and quadrilaterals : a quadrilateral ...
I. Parallelogram: definition and properties. Def 1: A parallelogram is a quadrilateral with two pairs of parallel sides.
Attention: big mistake: do not mix up parallelograms and quadrilaterals : a quadrilateral has 4 sides with absolutely no particularity a priori.
Pty 1: If a quadrilateral is a parallelogram, then his opposite sides are equal in length. Pty 1’: If the two pairs of opposite sides of a quadrilateral are equal in length, then it’s a parallelogram. Comment: Pty 1’ is the reverse of Pty 1. Application: construction of a parallelogram using the ruler and compass.
Pty 2: If a quadrilateral is a parallelogram, then his diagonals bisect* each other. Each diagonal crosses the other in its midpoint. Pty 2’: If the diagonals of a quadrilateral bisect each other, then it’s a parallelogram. Comment: The point where the diagonals cross each other is the symmetry centre of the parallelogram.
Pty 3: I f a quadrilateral is a parallelogram, then its opposite angles are equal in measure
II.
Area of a parallelogram.
http://www.mathgoodies.com/LESSONS/vol1/area_parallelogram.html Def 2: In a parallelogram ABCD, a height with respect to the side [AB] is a segment line, perpendicular to [AB], that joins [AB] and its opposite side [CD]. The length of this segment line is also called “height”.
Pty 4: To calculate the area of a parallelogram you use the length “c” of one of its sides, and the length “h” of the height with respect to that side, in the formula: A = c × h .
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Gr11 Lesson 2. Vectors and parallelogram. The parallelogram and its properties. 1. Definition: A parallelogram ABCD is a quadrilateral such that the segment ...
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