Question

1. what is the statement and reason for a?

given:abcd is a rectangle
prove: abcd is a parallelogram; \\( \overline { a c } \cong \overline { b d } \\)
abcd is a rectangle
given
\\( \overline { a d } \cong \overline { b c } \\)
opposite sides of a parallelogram are congruent
\\( \overline { d c } \cong \overline { d c } \\)
reflexive property
a
abcd is a parallelogram
opposite angles of a parallelogram are congruent
\\( \delta a d c \cong \delta b c d \\)
sas
\\( \angle a \cong \angle c , \angle b \cong \angle d \\)
all right angles are congruent
\\( a c \cong b d \\)
cpctc

Explanation:

Step1: Analyze the given information and the flow of the proof

We know that \(ABCD\) is a rectangle (given). A rectangle is a quadrilateral with four right angles.

Step2: Determine the property of a rectangle related to the next step in the proof

Since a rectangle has four right angles, we can state that \(\angle A=\angle B=\angle C = \angle D = 90^{\circ}\)

Answer:

Statement: \(\angle A=\angle B=\angle C=\angle D = 90^{\circ}\); Reason: Definition of a rectangle (a rectangle has four right angles)