Using Congruent Triangle Criteria to Prove Diagonal Bisecting in a Rhombus

This lesson covers the use of congruence criteria in writing a proof, focusing on the CPCTC theorem and the properties of a rhombus. The core lesson involves proving that the diagonals of a rhombus bisect its angles using a two-column proof. The proof demonstrates congruence of triangles formed by the diagonals and uses the side-side-side postulate to establish congruence. The lesson concludes by confirming that the diagonals bisect the angles of the rhombus.

What does the CPCTC theorem state about congruent triangles?

• Their corresponding sides and angles are congruent.

• They are similar but not congruent.

• Their areas are equal.

• They have the same perimeter.

What is the defining characteristic of a rhombus?

• It has four right angles.

• It has four congruent sides.

• It has two pairs of parallel sides.

• It has one pair of parallel sides.

What is the purpose of drawing an auxiliary line in the proof?

• To measure the angles of the rhombus.

• To create two triangles for comparison.

• To divide the rhombus into four smaller rhombuses.

• To find the perimeter of the rhombus.

Which postulate is used to prove the congruence of triangles in the rhombus?

• Side-Side-Side (SSS) Postulate

• Side-Angle-Side (SAS) Postulate

• Angle-Side-Angle (ASA) Postulate

• Angle-Angle-Side (AAS) Postulate

What conclusion is reached about the diagonals of a rhombus?

• They are equal in length.

• They bisect each other.

• They are perpendicular to each other.

• They bisect the angles of the rhombus.