Bot GPT 4-o mini To determine the value of \( x \) that makes triangles \( FGH \) and \( KJH \) congruent by the Side-Side-Side (SSS) postulate, we need to set the lengths of the corresponding sides equal to each other.
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We'll denote the lengths:
- \( FH = HK \)
- \( GH = JH \)
- \( FG = JK \)
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We know that the lengths of sides \( FG \) and \( JK \) are given as:
- \( FG = 3x - 2 \)
- \( JK = 2x + 4 \)
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For the triangles to be congruent, we set \( FG \) equal to \( JK \): \[ 3x - 2 = 2x + 4 \]
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Now, we'll solve for \( x \):
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Subtract \( 2x \) from both sides: \[ 3x - 2x - 2 = 4 \] \[ x - 2 = 4 \]
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Add 2 to both sides: \[ x = 6 \]
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Thus, \( x \) must be \( 6 \) for the triangles \( FGH \) and \( KJH \) to be congruent by SSS.
Answer: 6
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