U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

~=

X

Y

Z~=~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given

~=

XS

Y

Z~=

~=

~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given

~=

~=

XS

Y

Z~=

~=

~=

S

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given 3. XZ XZ 3. Ref.

~=

~=~=

XS

Y

Z~=

~=

~=

SS

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given 3. XZ XZ 3. Ref.4. XYZ XWZ 4. SSS

~=

~=~=

X

~=

S

Y

Z~=

~=

~=

SS

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given 3. XZ XZ 3. Ref.4. XYZ XWZ 4. SSS

~=

~=~=

X

~=

S

Y

Z~=

~=

~=

SS

S

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given 3. XZ XZ 3. Ref.4. XYZ XWZ 4. SSS5. YZU WZU 5. CPCTC

~=

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X

~=

S

Y

Z~=

~=

~=

A

~=

SS

S

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given 3. XZ XZ 3. Ref.4. XYZ XWZ 4. SSS5. YZU WZU 5. CPCTC6. ZU ZU 6. Ref.

~=

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X

~=

S

Y

Z~=

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~=

A

~=

SS

~=

S

S

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given 3. XZ XZ 3. Ref.4. XYZ XWZ 4. SSS5. YZU WZU 5. CPCTC6. ZU ZU 6. Ref.7. YZU WZU 7. SAS

~=

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X

~=

S

Y

Z~=

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~=

A

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S

S~=

U W

Given: YZ WZ XY XW Prove: UYZ UWZ

ProofStatement Reason

1. YZ WZ 1. Given 2. XY AC 2. Given 3. XZ XZ 3. Ref.4. XYZ XWZ 4. SSS5. YZU WZU 5. CPCTC6. ZU ZU 6. Ref.7. YZU WZU 7. SAS8. UYZ UWZ 8. CPCTC

~=

~=~=

X

~=

S

Y

Z~=

~=

~=

A

~=

SS

~=

S

S~=~=

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

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B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given

~=~= A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint

~=

~=

~=

S

A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint

~=

~=~=

~=

SS

A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles

~=

~=~=

~=

~=

A

SS

A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS

~=

~=~=

~=~=

~=

A

SS

A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC

~=

~=~=

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~=

A

SS

S

A

B

C DE

G

F

~=

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC7. BCD GED 7. CPCTC

~=

~=~=

~=~=

~=

A

SS

~=S~=

A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC7. BCD GED 7. CPCTC8. ACB supp. to BCD 8. linear pair

~=

~=~=

~=~=

~=

A

SS

~=S~=

A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC7. BCD GED 7. CPCTC8. ACB supp. to BCD 8. linear pair9. FEG supp. to GED 9. linear pair

~=

~=~=

~=~=

~=

A

SS

~=S~=

A

B

C DE

G

F

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC7. BCD GED 7. CPCTC8. ACB supp. to BCD 8. linear pair9. FEG supp. to GED 9. linear pair10. ACB FEG 10. 's supp. to to 's are .

~=

~=~=

~=~=

~=

A

~=

SS

~=S

~=

~=

A

B

C DE

G

F

~=A

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC7. BCD GED 7. CPCTC8. ACB supp. to BCD 8. linear pair9. FEG supp. to GED 9. linear pair10. ACB FEG 10. 's supp. to to 's are .11. ABC FGE 11. Given

~=

~=~=

~=~=

~=

A

~=

SS

~=S

~=

~=

A

B

C DE

G

F

~=AA ~=

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC7. BCD GED 7. CPCTC8. ACB supp. to BCD 8. linear pair9. FEG supp. to GED 9. linear pair10. ACB FEG 10. 's supp. to to 's are .11. ABC FGE 11. Given12. ACB FEG 12. ASA

~=

~=~=

~=~=

~=

A

~=

SS

~=S

~=

~=

A

B

C DE

G

F

~=AA ~=

~=

Given: D is midpoint of CE and BG ABC FGEProve: AB FG Proof

Statement Reason1. D is mdpt. of CE, BG 1. Given 2. CD ED 2. Def. of midpoint 3. BD GD 3. Def. of midpoint4. CDB EDG 4. Vert. angles5. BCD EGD 5. SAS6. BC GE 6. CPCTC7. BCD GED 7. CPCTC8. ACB supp. to BCD 8. linear pair9. FEG supp. to GED 9. linear pair10. ACB FEG 10. 's supp. to to 's are .11. ABC FGE 11. Given12. ACB FEG 12. ASA13. AB FG 13. CPCTC

~=

~=~=

~=~=

~=

A

~=

SS

~=S

~=

~=

A

B

C DE

G

F

~=AA ~=

~=~=

In this lesson we looked at detour proofs.

In these proofs we proved a pair of triangles congruent

before using CPCTC to prove a second pair of triangles

congruent.