Transcript Quadrilateral Proofs

Quadrilateral
Proofs
Page 6
Pg. 6 #1
Pg. 6 #3
Statement
L
4
F
1
G
A
2
3
H
S
Reason
1. FLSH is a parallelogram
1. Given
2. LG  FS
2. Given
3. HA  FS
4. 1 and 2 are
right angles
3. Given
5. 1  2
5. All right angles are congruent
6. LS FH and LS  FH
6. Opposite sides of a
parallelogram are both parallel
and congruent
7. 3  4
7. Parallel lines cut by a
transversal form congruent
alternate interior angles
8. ΔLGS  ΔHAF
8. AAS  AAS
4. Perpendicular segments form
right angles
Pg. 7 #7
Statement
D
C
2
A
B
Reason
1. ABCD is a parallelogram
1. Given
2. AD BC
2. Opposite sides of a
parallelogram are parallel
3. BCA  2
3. Parallel lines cut by a
transversal form congruent
alternate interior angles
4. 1  BCA
4. An exterior angle of a
triangle is greater than either of
its non-adjacent interior angles
5. 1  2
5. Substitution postulate of
inequalities
1
Pg. 7
Statement
V
D
1
B 3
4 S
2
T
Reason
1. DCTV is a parallelogram
1. Given
2. BC VS
2. Given
3. VST  DBC
3. Parallel lines cut by a
transversal form congruent
alternate interior angles
4. VT DC andVT  DC
4. Opposite sides of a
parallelogram are both parallel
and congruent
5. 3  4
5. Parallel lines cut by a
transversal form congruent
alternate interior angles
6. ΔVST  ΔCBD
6. AAS  AAS
7. 1  2
7. CPCTC
C
Prove : 1  2
Pg.
Statement
F
D
C
1
3
E
4
2
A
G
Reason
1. ABCD is a parallelogram
1. Given
2. FG bisects DB
2. Given
3. DE  EB
3. A segment bisector divides a
segment into 2 congruent parts
4. AB DC
4. Opposite sides of a
parallelogram are parallel
5. 1  2
5. Parallel lines cut by a
transversal form congruent
alternate interior angles
6. 3  4
6. Vertical angles are congruent
7. ΔDEF  ΔBEG
7. ASA  ASA
8. FE  EG
8. CPCTC
B
Prove: FE  EG
Pg.
Statement
D
F
4
A
1
C
2
E
B
3
Reason
1. ABCD is a parallelogram
1. Given
2. DE  AC
3. BF  AC
2. Given
3. Given
4. 1 and 2 are
right angles
4. Perpendicular segments form
right angles
5. 1  2
5. All right angles are congruent
6. DA CB , DA  CB
6. Opposite sides of a
parallelogram are both congruent
and parallel.
7. 3  4
7. Parallel lines cut by a
transversal form congruent
alternate interior angles
8. ΔDEA  ΔBFC
8. AAS  AAS
9. AE  FC
9. CPCTC
Prove: AE  FC
Pg.
Statement
D
C
F
1
A
2
E
Reason
1. ABCD is a parallelogram
1. Given
2. AE  FC
2. Given
3. DA CB , DA  CB
3. Opposite sides of a
parallelogram are both congruent
and parallel.
4. 1  2
4. Parallel lines cut by a
transversal form congruent
alternate interior angles
5. ΔADE  ΔBFC
5. SAS  SAS
B
Prove : ADE  BFC
Pg.
Statement
D
F
4
A
1
C
2
E
B
3
Reason
1. ABCD is a quadrilateral
1. Given
2. DE  AC , BF  AC
2. Given
3. AE  CF , DE  BF
4. 1 and 2 are
right angles
3. Given
4. Perpendicular segments form
right angles
5. 1  2
5. All right angles are congruent
6. ΔDEA  ΔBFC
6. SAS  SAS
7. 3  4
7. CPCTC
8. DA  CB
8. CPCTC
9. DA CB
9. 2 lines cut by a transversal that
form congruent alternate interior
angles are parallel
10. A quadrilateral with one pair of
opposite sides both congruent and
parallel is a parallelogram
10. ABCD is a parallelogram
Prove: ABCD is a parallelogram
B
Pg.
3
D
Statement
E
F
4
A
C
Reason
1. D is the midpoint of AB
1. Given
2. DF and BC bisect
each other
3. AD  DB
2. Given
4. DE  EF
BE  EC
3. A midpoint divides a segment
into 2 congruent parts
4. A segment bisector divides a
segment into 2 congruent parts
5. 1  2
5. Vertical angles are congruent
6. ΔBED  ΔCEF
6. SAS  SAS
7. 3  4
7. CPCTC
8. ADB CF
8. 2 lines cut by a transversal that
form congruent alternate interior
angles are parallel
9. DB  FC
10. AD  FC
9. CPCTC
11. ACFD is a parallelogram
Prove: ACFD is a parallelogram
10. Substitution postulate
11. A quadrilateral with one pair of
opposite sides both congruent and
parallel is a parallelogram