Download Special Parallelograms Proofs Practice Name: Period: ______ C D

Special Parallelograms Proofs Practice
Name: __________________________ Period: _______
1. Given: ABCD is a parallelogram. ∠A is a right angle.
Prove: ABCD is a rectangle.
A
D
B
Statements
1. ABCD is a parallelogram.
 A is a right angle
2. mA  90
C
Reasons
1.
2. Definition of right 
3. A and B are supplementary
3.
4.
4. Definition of supplementary  ' s
5. 90  mB  180
5.
6.
6. Subtraction Property of =
7. C  A, D  B
7.
8. mC  mA, mD  mB
8.
9. mC  90 , mD  90
9. Transitive Property of =
10. B, C , D are right angles
10. Definition of right  ' s
11.
11. Definition of rectangle
2. Given: ABCD is a parallelogram. AC  BD
Prove: ABCD is a rectangle.
A
D
B
C
Statements
Reasons
1.
1. Given
2. AB  CD
2.
3.
3. Reflexive property of =
4.
BAC  CDB
4.
5. ABC  DCB
5.
6. ABC and DCB are supplementary
6.
7. ABC and DCB are right angles
7.   ' s that are supplementary  right  ' s
8.
8. Parallelogram with one right   rectangle
3. Given: ABCD is a parallelogram. AB  AD .
Prove: ABCD is a rhombus.
Statements
1.
ABCD is a parallelogram. AB  AD .
Reasons
1.
2.
2. Opposite sides of a parallelogram are 
3. AB  BC
3.
4.
4. Since AB is  to the other 3 sides of a
parallelogram, ABCD is a rhombus
4. Given: ABCD is a parallelogram. BD is perpendicular to AC .
Prove: ABCD is a rhombus.
E
5. Given: ABCD is a parallelogram. BD bisects ABC and CDA
Prove: ABCD is a rhombus.
Statements
1. ABCD is a parallelogram.
Reasons
1.
BD bisects ABC and CDA
2.
2. Definition of  bisector
3.
3. Reflexive property of =
4.
ABD  CBD
4.
5. AB  CB
5.
6.
6. Parallelogram with one pair of consecutive
sides   rhombus
6. Given: ABCD is a parallelogram. AB  BC , AC  BD
Prove: ABCD is a square.
Always, Sometimes, or Never
Decide if the following statements are always, sometimes, or never true. If you answer…
Always: Briefly explain why you believe this to be true.
Sometimes: Provide an example and a counterexample.
Never: Briefly explain why you believe the statement is never true.
1. A rectangle has consecutive complementary angles.
2. A parallelogram has congruent opposite angles.
3. A rhombus has four congruent angles.
4. A square has perpendicular diagonals.
5. A quadrilateral has at least one pair of congruent angles.
6. A parallelogram has congruent diagonals.
7. The diagonals of a rhombus divide the rhombus into two acute and two obtuse triangles.
8. Consecutive sides of a parallelogram are congruent.
9. Any two angles in a parallelogram are either congruent or supplementary.
10. A quadrilateral that is both a rhombus and a rectangle is a square.