Questions: between k and m. In the diagram, a reflection in line k maps GH to G'H'. A reflection in line n maps G'H' to G''H''. Also, HB=9 and DH''=4. a. Name any segments congruent to each segment: GH, HB, and GA. b. Does AC=BD ? Explain.

between k and m.
In the diagram, a reflection in line k maps GH to G'H'. A reflection in line n maps G'H' to G''H''. Also, HB=9 and DH''=4.
a. Name any segments congruent to each segment: GH, HB, and GA.
b. Does AC=BD ? Explain.
Transcript text: between $k$ and $m$. In the diagram, a reflection in line $k$ maps $\overline{G H}$ to $\overline{G^{\prime} H^{\prime}}$. A reflection in line $n$ maps $\overline{G^{\prime} H^{\prime}}$ to $\overline{G^{\prime \prime} H^{\prime \prime}}$. Also, $H B=9$ and $D H^{\prime \prime}=4$. a. Name any segments congruent to each segment: $\overline{G H}, \overline{H B}$, and $\overline{G A}$. b. Does $A C=B D$ ? Explain.
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Solution

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Solution Steps

Step 1: Identify Congruent Segments
  • GH is congruent to G'H' because reflection in line \( k \) maps \( GH \) to \( G'H' \).
  • G'H' is congruent to G"H" because reflection in line \( m \) maps \( G'H' \) to \( G"H" \).
  • HB is congruent to DH" because \( HB = 9 \) and \( DH" = 4 \).
Step 2: Determine if AC = BD
  • Since \( A \) and \( C \) are reflections of \( B \) and \( D \) respectively, and reflections preserve distances, \( AC \) should be equal to \( BD \).

Final Answer

  • Congruent segments: \( GH \cong G'H' \cong G"H" \), \( HB \cong DH" \).
  • Yes, \( AC = BD \) because reflections preserve distances.
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