Questions: Triangle EFI is congruent to triangle GFH. Complete the proof that triangle GHI is congruent to triangle EIH. - Statement Reason 1. Triangle EFI is congruent to triangle GFH 2. Line segment EI is congruent to line segment GH 3. Line segment EF is congruent to line segment FG 4. Line segment FI is congruent to line segment FH 5. EH = EF + FH 6. GI = FG + FI 7. EH = FG + FI 8. EH = GI 9. Line segment HI is congruent to line segment HI 10. Triangle GHI is congruent to triangle EIH

Triangle EFI is congruent to triangle GFH. Complete the proof that triangle GHI is congruent to triangle EIH.

- Statement  Reason
1. Triangle EFI is congruent to triangle GFH  
2. Line segment EI is congruent to line segment GH  
3. Line segment EF is congruent to line segment FG  
4. Line segment FI is congruent to line segment FH  
5. EH = EF + FH  
6. GI = FG + FI  
7. EH = FG + FI  
8. EH = GI  
9. Line segment HI is congruent to line segment HI  
10. Triangle GHI is congruent to triangle EIH
Transcript text: $\triangle E F I \cong \triangle G F H$. Complete the proof that $\triangle G H I \cong \triangle E I H$. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $\triangle E F I \cong \triangle G F H$ & \\ 2 & $\overline{E I} \cong \overline{G H}$ & \\ 3 & $\overline{E F} \cong \overline{F G}$ & $\square$ \\ 4 & $\overline{F I} \cong \overline{F H}$ & \\ \hline 5 & $E H=E F+F H$ & \\ \hline 6 & $G I=F G+F I$ & $\square$ \\ 7 & $E H=F G+F I$ & $\square$ \\ \hline 8 & $E H=G I$ & $\square$ \\ \hline 9 & $\overline{H I} \cong \overline{H I}$ & $\square$ \\ \hline 10 & $\triangle G H I \cong \triangle E I H$ & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Reason for Statement 1

Given

Step 2: Reason for Statement 2

Corresponding parts of congruent triangles are congruent (CPCTC)

Step 3: Reason for Statement 3

CPCTC

Step 4: Reason for Statement 4

CPCTC

Step 5: Reason for Statement 5

Segment Addition Postulate

Step 6: Reason for Statement 6

Segment Addition Postulate

Step 7: Reason for Statement 7

Substitution Property of Equality (Statements 3, 4, and 5)

Step 8: Reason for Statement 8

Substitution Property of Equality (Statements 6 and 7)

Step 9: Reason for Statement 9

Reflexive Property of Congruence

Step 10: Reason for Statement 10

SSS Congruence Postulate

Final Answer

  1. Given
  2. CPCTC
  3. CPCTC
  4. CPCTC
  5. Segment Addition Postulate
  6. Segment Addition Postulate
  7. Substitution Property of Equality
  8. Substitution Property of Equality
  9. Reflexive Property of Congruence
  10. SSS Congruence Postulate
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