Three figures exist such that $$ A B C D \cong G H I J $$ and $$ B C D A \cong R S T U $$. If $$ G H=6 \mathrm{~cm}, \mathrm{HI}=8 \mathrm{~cm}, I J=10 \mathrm{~cm} $$, and $$ G J=9 \mathrm{~cm} $$, what is $$ T S $$ ? 6 cm 8 cm 9 cm 10 cm

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UpStudy AI · Accepted Answer

To solve the problem, let's analyze the given information step by step.

1. **Understanding the Congruence:**
   - We are given that quadrilateral $$ A B C D $$ is congruent to $$ G H I J $$, so each corresponding side is equal.
   - Similarly, quadrilateral $$ B C D A $$ is congruent to $$ R S T U $$.

2. **Mapping the Sides:**
   - From $$ A B C D \cong G H I J $$:
     - $$ A $$ corresponds to $$ G $$
     - $$ B $$ corresponds to $$ H $$
     - $$ C $$ corresponds to $$ I $$
     - $$ D $$ corresponds to $$ J $$
     - So, $$ A B = G H = 6 $$ cm, $$ B C = H I = 8 $$ cm, $$ C D = I J = 10 $$ cm, and $$ D A = J G = 9 $$ cm.

3. **Determining $$ T S $$:**
   - From $$ B C D A \cong R S T U $$:
     - $$ B $$ corresponds to $$ R $$
     - $$ C $$ corresponds to $$ S $$
     - $$ D $$ corresponds to $$ T $$
     - $$ A $$ corresponds to $$ U $$
     - Thus, $$ D C $$ in $$ A B C D $$ corresponds to $$ T S $$ in $$ R S T U $$.

4. **Matching the Lengths:**
   - Since $$ C D = 10 $$ cm in $$ A B C D $$, this means $$ T S = 10 $$ cm in $$ R S T U $$.

**Final Answer:**  
10 cm
$$ T S = 10 $$ cm

Three figures exist such that and .
If , and , what is ?
6 cm
8 cm
9 cm
10 cm

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Three figures exist such that and . If , and , what is ? 6 cm 8 cm 9 cm 10 cm