Complete the paragraph proof of the Properties of Rectangles Theorems. Given: ABCD is a rectangle.
Prove: ABCD is a parallelogram; AC BD
А
B
D
Proof that ABCD is a parallelogram: Since ABCD is a rectangle, ZA and 2C are right angles. So,
ZA < 2C because (select)y right angles are congruent. By similar reasoning ZB = ZD. Therefore
ABCD is a parallelogram because it is a quadrilateral in which both pairs of opposite (select)
congruent
are
Proof that the diagonals are congruent: Since ABCD is a parallelogram, AD = BC because opposite
(select)y of a parallelogram are congruent. Also, DC = DC by the Reflexive Property of Congruence. By
the definition of a rectangle, 2C and ZD are right angles, and so ZC = ZD because (select) v right
angles are congruent. Therefore, AADC & ABCD by the (select)y Triangle Congruence Theorem and
AC BD by CPCTC.