Download Unit 5 - Day 4 - CW (Answers to Proofs)

Names:____________________________________________
Monica
Geometry Period:____
Date:___________________________
Prove that the following conjecture is true: The non-vertex angles of a kite are congruent.
Given: ABCD is a kite
Prove: A  C
B
A
C
D
STATEMENTS
1) ABCD is a kite
2) AB  CB
REASONS
1) Given
2) Definition of a kite
3) AD  CD
3) Definition of a kite
4) BD  BD
5) ABD  CBD
6) A  C
4) Reflexive Property
5) SSS
6) CPCTC
Names:____________________________________________
Monica
Geometry Period:____
Date:___________________________
Prove that the following conjecture is true: The diagonal connecting the vertex angles of a kite is the bisector of the other
diagonal.
Given: ABCD is a kite
Prove: AE  CE
B
A
E
C
D
STATEMENTS
1) ABCD is a kite
2) AB  CB
3) ABE  CBE
4) BE  BE
5) ABE  CBE
6) AE  CE
REASONS
1) Given
2) Definition of a kite
3) The diagonal bisects the vertex angles
4) Reflexive Property
5) SAS
6) CPCTC
Names:____________________________________________
Monica
Geometry Period:____
Date:___________________________
Prove that the following conjecture is true: The vertex angles of a kite are bisected by the diagonal.
Given: ABCD is a kite
Prove: ABE  CBE and ADE  CDE
B
A
E
C
D
STATEMENTS
1) ABCD is a kite
2) AB  CB
REASONS
1) Given
2) Definition of a kite
3) AD  CD
3) Definition of a kite
BD  BD
4) Reflexive Property
4)
5)
6)
7)
ABD  CBD
ABD  CBD
ADB  CDB
5) SSS
6) CPCTC
7) CPCTC
Names:____________________________________________
Monica
Geometry Period:____
Date:___________________________
Prove that the following conjecture is true: The diagonals of a kite are perpendicular.
Given: ABCD is a kite
Prove: AEB is a right angle
B
A
E
C
D
STATEMENTS
1) ABCD is a kite
2) AB  CB
3) ABE  CBE
4) BE  BE
5) ABE  CBE
6) AEB  CEB
7) AEB  CEB  180
8) AEB  AEB  180
9) 2AEB  180
10) AEB  90
11) AEB is a right angle
REASONS
1) Given
2) Definition of a kite
3) The diagonal bisects the vertex angles
4) Reflexive Property
5) SAS
6) CPCTC
7) Definition of supplementary angles
8) Substitution
9) Simplify
10) Division Property
11) Definition of a right angle
Names:____________________________________________
Monica
Geometry Period:____
Date:___________________________
Prove that the following conjecture is true: The opposite angles in an isosceles trapezoid are supplementary.
Given: ABCD is an isosceles trapezoid
Prove:
A and C are supplement ary
B and D are supplement ary
A
B
D
C
STATEMENTS
1) ABCD in an isosceles trapezoid
2) A  B
3) A and D are supplement ary
4) B and D are supplement ary
5) D  C
6) B and C are supplement ary
7) B and D are supplement ary
REASONS
1)
2)
3)
4)
5)
6)
7)
Given
Base angles in an isosceles trapezoid are congruent
Consecutive angles in an isosceles trapezoid are congruent
Substitution
Base angles in an isosceles trapezoid are congruent
Consecutive angles in an isosceles trapezoid are congruent
Substitution
Names:____________________________________________
Monica
Geometry Period:____
Date:___________________________
Prove that the following conjecture is true: The diagonals of an isosceles trapezoid are congruent.
Given: ABCD is an isosceles trapezoid
Prove: DB  CA
A
B
D
C
STATEMENTS
1) ABCD in an isosceles trapezoid
2) AD  BC
3) D  C
4) DC  CD
5) ADC  BCD
6) DB  CA
REASONS
1) Given
2) Definition of an isosceles trapezoid
3) Base angles in an isosceles trapezoid are congruent
4) Reflexive Property
5) SAS
6) CPCTC