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The main properties of parallelograms are outlined in this section, emphasizing how diagonals bisect each other, opposite sides are equal, and opposite angles are congruent. The section also includes various theorems that prove these properties and provides examples for better understanding.
In this section, we explore the distinctive characteristics of parallelograms, a special type of quadrilateral where both pairs of opposite sides are parallel. A significant activity involves cutting a parallelogram along a diagonal to demonstrate that it divides into two congruent triangles, unveiling the first theorem about the congruence of these triangles.
Examples provided illustrate how these properties manifest in specific quadrilaterals, such as rectangles and rhombuses. Exercises reinforce understanding of these concepts by applying them in various mathematical scenarios.
Congruency of Triangles: Understanding how diagonals separate a parallelogram into two equal triangles.
Equality of Opposite Sides: A parallelogram's opposite sides are always equal, leading to special properties.
In a parallelogramβs view, opposite sides are equal too.
Imagine a party where pairs of friends stand opposite each other, holding hands, never letting go. Their lengths are equalβa perfect parallelogram party!
Remember 'PEACE' for Parallelogram Opposite Equal Angles & Sides.
Term: Parallelogram
Definition: A quadrilateral with both pairs of opposite sides parallel.
A quadrilateral with both pairs of opposite sides parallel.
Term: Diagonals
Definition: Line segments connecting non-adjacent vertices of a polygon.
Line segments connecting non-adjacent vertices of a polygon.
Term: Congruent
Definition: Figures that have the same size and shape.
Figures that have the same size and shape.
Term: Alternate Angles
Definition: Angles that are on opposite sides of a transversal and in matching corners.
Angles that are on opposite sides of a transversal and in matching corners.