Question

Prove that the diagonals of a parallelogram (a shape with two pairs of equal length sides, with the sides within a pair being opposite of each other, and running along parallel lines) partition the parallelogram into congruent triangles.

Answer 1

To prove that the diagonals partition a parallelogram into congruent triangles, one must understand that a parallelogram's diagonals split it into triangles that are congruent due to the SSS congruence postulate.

Step-by-step explanation:

The question involves proving that the diagonals of a parallelogram partition it into congruent triangles. By definition, a parallelogram has two pairs of parallel sides, and opposite sides of a parallelogram are equal in length. When we draw one of the diagonals in a parallelogram, it intersects with the opposite sides at their midpoints, effectively splitting the parallelogram into two triangles. Moreover, these triangles are congruent due to the Side-Side-Side (SSS) congruence postulate, as they share one side (the diagonal itself), and the parallelogram's opposite sides are congruent to each other. Therefore, drawing both diagonals partitions the parallelogram into four congruent triangles by the same principle since each diagonal creates a pair of congruent triangles.