1. Complete the following statement so that it is true.
A parallelogram is a rectangle if and only if its diagonals are-------------
Congruent
Perpendicular
Intersecting
Parallel
2. Consider parallelogram ABCD . Which triangles, if congruent, could be used to prove the diagonals are congruent?
A. I only
B. II only
C. I,II and III
D. I and II
3. Several students in a class made the following statement. Decide whether you agree with the statement. If you disagree, change the statement to make it correct. A quadrilateral with congruent diagonals must be a rectangle.
A. Agree
B. Disagree. A parallelogram with congruent diagonals must be a rectangle.
C. Disagree. A quadrilateral with one right angle must be a rectangle.
D. Disagree. A quadrilateral with two pairs of opposite parallel sides must be a rectangle.
4. Consider parallelogram ABCD . Given the following information, is the parallelogram also a rectangle?
AB¯¯¯¯¯¯¯¯=3x+1
BD¯¯¯¯¯¯¯¯=4x
CD¯¯¯¯¯¯¯¯=5x−5
AD¯¯¯¯¯¯¯¯=6x−3
A. There is not enough information given to answer this question.
B. Yes, because BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯
C. No, because AC¯¯¯¯¯¯¯¯≆BD¯¯¯¯¯¯¯¯
D. Yes, because AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯
1. A parallelogram is a rectangle if and only if its diagonals are perpendicular.
2. D. I and II
3. B. Disagree. A parallelogram with congruent diagonals must be a rectangle.
4. A. There is not enough information given to answer this question.