Given: Rhombus ABCD
<10 = <9
Prove: AECF is a
B
E
A
3 4
7
2
10
9
1
D
1.
2.
3.
4.
5.
6.
7.
8.
Statements
ABCD is a rhombus
<10 = <9
AD = BC
<1 = <2
ΔADF = ΔCBE
AF = EC
EB = DF
AB = DC
AE = FC
AECF is a
6 5
8
C
F
Reasons
1. Given
2.
3.
4.
5.
Opposite sides of a rhombus are =
Opposite <s of a rhombus are =
ASA
CPCTC
6. Same as 2
7. Segment subtraction property
8. Both pairs of opposite sides are =
Given: Rhombus ABCD
<10 = <9
(option 2)
Prove: AECF is a
B
E
A
3 4
7
2
10
9
1
D
1.
2.
3.
4.
5.
6.
7.
8.
9.
Statements
ABCD is a rhombus
<10 = <9
AD = BC
<1 = <2
ΔADF = ΔCBE
EB = DF
AB = DC
AE = FC
AB // DC
AECF is a
6 5
8
C
F
Reasons
1. Given
2.
3.
4.
5.
6.
7.
8.
9.
Opposite sides of a rhombus are =
Opposite <s of a rhombus are =
ASA
CPCTC
Same as 2
Segment subtraction property
Opposite sides of a rhombus are //
1 pair of opp sides both // and =
Given: Rhombus ABCD
<10 = <9
(option 3)
Prove: AECF is a
B
E
A
3 4
7
2
10
9
1
D
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Statements
ABCD is a rhombus
<10 = <9
AD = BC
<1 = <2
ΔADF = ΔCBE
<4 = <6
AB // DC
<7 = <6
<4 = <7
AF // EC
AECF is a
6 5
F
8
C
Reasons
1. Given
2. Opposite sides of a rhombus are =
3. Opposite <s of a rhombus are =
4. ASA
5. CPCTC
6. Opposite sides of a rhombus are //
7. // lines  alt int <s =
8. Transitive property
9. Corr <s =  // lines
10. Both pairs opp sides are //
Given: ABCD is an isosceles trapezoid
<1 = <7
Prove: EFCD is an isosceles trapezoid
A
E
D
2
8
3
7
4
6
2.
3.
4.
Statements
ABCD is an isos trap
<1 = <7
AB // CD
AB // EF
EF // DC
5.
6.
7.
<5 = <6
EFCD is a trapezoid
EFCD is an isos trap
1.
1
B
F
5
C
Reasons
1. Given
2. Given/def trap
3. Corr <s =  // lines
4. If 2 lines are // to a 3rd, they are // to each
Other
5. Base <s of an isos trap are =
6. 1 pair of opp sides //
7. A trap with a pair of base <s = is isosceles
Given: ABCD is an isosceles trapezoid
AE and BF are perpendicular to CD
Prove: ABFE is a rectangle
D
6
A
2
7 8
34
E
F
2.
3.
Statements
ABCD is an isosceles trap
AE and BF are perp to CD
<s3, 4, 7, & 8 are right <s
AE // BF
4.
5.
6.
AB // EF
ABFE is a parallelogram
ABFE is a rectangle
1.
1
B
5
C
Reasons
1. Given
2. Def perpendicular
3. In a plane, if 2 lines are perpendicular to a
3rd, then they are // to each other
4. Given/def trap
5. 2 prs opp sides =
6. A parallelogram with 1 rt < is a rectangle
Given: ABCD is an isosceles trapezoid
AE and BF are perpendicular to CD
Prove: ABFE is a rectangle
D
6
A
1
2
B
7 8
34
E
F
2.
3.
Statements
ABCD is an isosceles trap
AE and BF are perp to CD
AB // CD
AE and BF are perp to AB
4.
5.
<s 1, 2, 3, & 8 are rt <s
ABFE is a rectangle
1.
(option 2)
5
C
Reasons
1. Given
2. Given/def trap
3. In a plane, if a line is perp to one of 2 //
lines, it is perp to the other.
4. Def perpendicular
5. A quadrilateral with 4 right <s is a rectangle