Download geo 4-3 and 4

Geometry Homework – 4-3 and 4-4
Name:
Date:
1)
Developing Proof Complete the two-column proof by
filling in the blanks.
Given: BD  AC, BD bisects ABC
Prove: ∆ABD  ∆CBD
Statements
Reasons
1) BD  AC, BD bisects ABC
1) Given
2)
2) Definition of perpendicular
3) ADB  CDB
3)
4) ABD  CBD
4)
5)
6)
5) Reflexive Property of 
6) ASA
Given: KJ  MN , KJL  MNL
Prove: ∆JKL  ∆NML
2)
Statements
1) KJ  MN , KJL  MNL
Reasons
1) Given
2) KLJ  MLN
2)
3)
3) AAS
Given: BD is the angle bisector of ABC and ADC.
Prove: ∆ABD  ∆CBD
3)
Statements
Reasons
1)
1)
2)
2) Definition of  bisector
3) BD  BD
3)
4)
4)
Block:
4)
Given: B and D are right angles; AE bisects BD
Prove: ABC  EDC
Statements
5)
Given: E  H; HFG  EGF
Prove: EGF  HFG
Statements
6)
Reasons
Reasons
Given: JM bisects J; JM  KL
Prove: JMK  JML
Statements
Reasons
Given: QS RT , R  S
7)
Prove: QTS  TQR
Statements
Reasons
1)
1) Given
2)
2) Alternate interior
3)
3) Reflexive Property of Congruence
4)
4) AAS
5)
5) Corresp. parts of 
8)
are .
are .
Given: GK is the perpendicular bisector of FH .
Prove: FG  HG
Statements
1) GK is the perpendicular bisector of FH .
2)
Reasons
1)
3) GKF  GKH
2) Def. of perpendicular bis.
3) Def. of perpendicular bis;
all right are .
4)
4) Refl. Prop. of 
5) ∆FGK  ∆HGK
5)
6)
6) Corresp. parts of 
are .
9) Complete the proof.
Given: BD  AB , BD  DE , BC  DC
Prove: A  E
Statements
Reasons
1) BD  AB , BD  DE
1)
2) CDE and CBA are right angles.
2) Definition of right angles
3) CDE  CBA
3)
4)
4) Vertical angles are congruent.
5) BC  DC
5)
6)
6)
7) A  E
7)
10) Complete the proof.
Given: YA  BA , B  Y
Prove: AZ  AC
Statements
1) YA  BA , B  Y
Reasons
1)
2) YAZ  BAC
2)
3)
3)
4)
4)