Quadrilateral Proofs - Camden Central School
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Transcript Quadrilateral Proofs - Camden Central School
Quadrilateral Proofs
Page 4-5
Pg. 4 #1
(a) One pair of opposite side both parallel and congruent
(b) Both pairs of opposite sides congruent
(c) Both pairs of opposite angles congruent
(d) Both pairs of opposite sides parallel
(e) Diagonals bisect each other
Pg. 4 #2
Statement
D
A
C 1. ABCD is a quadrilateral
2. AB CD
1
2
B
Reason
1. Given
2. Given
3. 1 2
3. Given
4. AB CD
4. Two lines cut by a transversal
that form congruent alternate
interior angles are parallel
5. ABCD is a parallelogram
5. A quadrilateral with one pair of
opposite sides that are both
parallel and congruent is a
parallelogram
Pg. 4 #3
Statement
Reason
1. PQRS is a quadrilateral
1. Given
2. 1 2
2. Given
3. 3 4
3. Given
4. SP RQ
4. Two lines cut by a transversal
that form congruent alternate
interior angles are parallel
PQ SR
5. PQRS is a parallelogram
5. A quadrilateral with both pairs of
opposite sides parallel is a
parallelogram
Pg. 4 #5
Statement
Reason
1. LM is a median
2. LM MJ
3. M is themidpointof KG
1. Given
4. KM MG
4. A midpoint divides a segment
into 2 congruent parts
5. GJKL is a parallelogram
5. A quadrilateral with diagonals that
bisect each other is a parallelogram
2. Given
3. A median extends from a vertex
of a triangle to the midpoint of the
opposite side
Pg. 4 #8
Statement
Reason
1. 2 is supplementary to1
1. Given
2. C 1
2. Given
3. 2 and DAB are
a linear pair
3. Two adjacent angles that form a
straight line are a linear pair
4. 2 and DAB are
supplementary
4. Linear pairs are
supplementary
5. 1 DAB
5. Supplements of the same
angle are congruent
6. DA CB
6. Two lines cut by a transversal
that form congruent corresponding
angles are parallel
7. AB DC
7. Two lines cut by a transversal
that form congruent alternate
interior angles are parallel
8. ABCD is a parallelogram
8. A quadrilateral with both pairs of
opposite sides parallel is a
parallelogram
Pg. 4 #12
Statement
Reason
1. PQRS is a parallelogram
1. Given
2. PE SQ
2. Given
3. RF SQ
4. 1 and 2 are
right angles
3. Given
5. 1 2
5. All right angles are congruent
6. SP RQ
SP RQ
6. Opposite sides of a
parallelogram are both parallel
and congruent
7. 3 4
4. Perpendicular segments form
right angles
7. Parallel lines cut by a
transversal form congruent
alternate interior angles
8. ΔPES ΔRFQ
8. AAS AAS
9. SE QF
9. CPCTC
Pg. 5 #1
Statement
Reason
1. ABCD is a rectangle
1. Given
2. M is themidpointof AB
2. Given
3. A B
3. All angles of a
rectangle are congruent
4. DA CB
4. Opposite sides of a
rectangle are congruent
5. AM MB
5. A midpoint divides a segment
into two congruent parts
6. MAD MBC
6. SAS SAS
7. DM CM
7. CPCTC
Pg. 5 #2
Statement
Reason
1. ABCD is a rectangle
1. Given
2. DA CB
2. Opposite sides of a
rectangle are congruent
3. AB AB
3. Reflexive postulate
4. DAB ABC
4. All angles of a rectangle are
congruent
5. DAB CBA
5. SAS SAS
6. 1 2
6. CPCTC
7. AEB is isosceles
7. A triangle with two congruent
base angles is isosceles
Pg. 5 #3
Statement
Reason
1. ABCD is a rhombus
1. Given
2. AE CE
3. AD DC
2. Given
4. DE DE
4. Reflexive postulate
5. ADE CDE
5. SSS SSS
6. ADE CDE
6. CPCTC
3. All sides of a rhombus
are congruent
Pg. 5 #4
Statement
Reason
1. AECB is a rhombus
1. Given
2. FAB DCB
2. Given
3. AE CE
3. All sides of a rhombus
are congruent
4. 1 2
4. Vertical angles are congruent
5. 3 4
5. Opposite angles of a rhombus
are congruent
6. FAB 3 DCB 4 6. Subtraction postulate
7. FAB 3 FAE
DCB 4 DCE
7. Partition postulate
8. DCE FAE
8. Substitution postulate
9. FAE DCE
9. ASA ASA
10. FE DE
10. CPCTC
Pg. 5 #8
Statement
Reason
1. ABCD is an isosceles
trapezoid
1. Given
2. DC // AB
2. Given
3. Base angles of an isosceles
trapezoid are congruent
3. DAB CBA
4. 1 and DAB are a linear pair
2 and CBA are a linear pair
4. Two adjacent angles that
form a straight line are a linear
pair
5. 1 and DAB are supplementary
2 and CBA are supplementary
6. 1 2
5. Linear pairs are
supplementary
6. Supplements of congruent
angles are congruent