Question 4 of 10
The proof shows that ABCD is a rectangle. Which of the
following is the missing reason?
B
C
A
D
Prove: ABCD is a rectangle
Statements
Reasons
1. ABCD is a parallelogram and ZA is
1. Given
a right angle.
2. mZA 90°
2. A right angle has a measure of
90°.
3. ZA ZC
3. Opposite angles of a
4.
mZC 90°
parallelogram are congruent.
Congruent angles have the same
m/A+mZB = 180°,
4.
5.
measure.
mZA+mZD=180°
5.
?
6. Substitution
90°+mZB=180°,
6.
90°+m/C=180°
7. Subtraction property of equality
8. A right angle has a measure of
90°.
7. m/B=90°, mZC = 90°
8. ZA, ZB, ZC, and ZD are right
angles.
9. By definition, a rectangle is a
quadrilateral with four right
angles.
9. Parallelogram ABCD is a
rectangle.
QED
A. Consecutive angles of a parallelogram are congruent.
B. Opposite angles of a parallelogram are congruent.
C. Consecutive angles of a parallelogram are complementary.
D. Consecutive angles of a parallelogram are supplementary.