WILL RATE THE BRAINLIST Explain how you can prove your observations in question 3 using a traditional proof. You don't need to d
evelop the steps of the proof; simply describe an approach that you might use. Which theorems might appear in your proof? (Hint: Use the two diagonals of the parallelogram to assist you in describing an approach.)
Rectangles are parallelograms. By definition, opposite sides are congruent and all four angles have the same measure. Drawing the two diagonals of a rectangle divides the rectangle into triangles. If I choose a pair of triangles that each have a different diagonal for a side, I can prove them to be congruent. If the triangles are congruent, the corresponding sides (diagonals of the rectangle in this case) are also congruent.
The two diagonals divide the parallelogram into four triangles. If I can prove that the two triangles opposite one another are congregant. then the corresponding sides of those two triangles must be congregant. These corresponding sides will help show that the lengths of the line segments on either side of the point of intersection are equal, proving bisection. To prove triangle congruency, I can use the properties of the angles formed when parallel lines are cut by a transversal and that opposite sides of the parallelogram are congregant.
