Proving Diagonal Properties in Parallelograms

This lesson covers the properties of diagonals in parallelograms and rectangles. It explains how to use parallel lines and triangle congruence theorems to prove that diagonals bisect each other in parallelograms and are congruent in rectangles. The lesson includes detailed proofs and emphasizes the unique properties of rectangles compared to other parallelograms.

What is the relationship between alternate interior angles when parallel lines are cut by a transversal?

• They are supplementary.

• They are congruent.

• They are complementary.

• They are equal to 90 degrees.

In a parallelogram, what can be said about the opposite sides?

• They are perpendicular.

• They are bisected by the diagonals.

• They are congruent.

• They are not equal.

Which congruence theorem is used to prove that diagonals bisect each other in a parallelogram?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Angle-Angle-Side (AAS)

What does CPCTC stand for in geometry?

• Congruent Parts of Corresponding Triangles are Complementary

• Corresponding Parts of Congruent Triangles are Complementary

• Congruent Parts of Corresponding Triangles are Congruent

• Corresponding Parts of Congruent Triangles are Congruent

What is a key property of diagonals in a rectangle?

• They are congruent.

• They are not equal.

• They bisect each other at right angles.

• They are perpendicular.

Which property of rectangles is used to prove that their diagonals are congruent?

• Diagonals are perpendicular.

• Opposite sides are parallel.

• Diagonals bisect each other.

• All angles are right angles.

If a parallelogram has congruent diagonals, what type of quadrilateral is it?

• A rectangle

• A square

• A trapezoid

• A rhombus