Question

given that the following triangles are congruent, determine the value of (x):

(x = 2)
(x = \frac{1}{5})
(x = 11)
(x = 5)

Explanation:

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<reasoning>

Identify corresponding parts of congruent triangles

\[

$$\begin{aligned} &\text{Left Triangle: side between right angle and double-arc angle} = 14\\ &\text{Right Triangle: side between right angle and double-arc angle} = 5x + 1\\ &\text{Corresponding sides are equal: } 5x + 1 = 11 \end{aligned}$$

\]

Solve the linear equation for x

\[

$$\begin{aligned} 5x + 1 &= 11\\ 5x &= 10\\ x &= 2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = 2\)</mcq-correct>
<mcq-option>(B) \(x = \frac{1}{5}\)</mcq-option>
<mcq-option>(C) \(x = 11\)</mcq-option>
<mcq-option>(D) \(x = 5\)</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
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"Triangle Congruence"
]
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Answer:

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<reasoning>

Identify corresponding parts of congruent triangles

\[

$$\begin{aligned} &\text{Left Triangle: side between right angle and double-arc angle} = 14\\ &\text{Right Triangle: side between right angle and double-arc angle} = 5x + 1\\ &\text{Corresponding sides are equal: } 5x + 1 = 11 \end{aligned}$$

\]

Solve the linear equation for x

\[

$$\begin{aligned} 5x + 1 &= 11\\ 5x &= 10\\ x &= 2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = 2\)</mcq-correct>
<mcq-option>(B) \(x = \frac{1}{5}\)</mcq-option>
<mcq-option>(C) \(x = 11\)</mcq-option>
<mcq-option>(D) \(x = 5\)</mcq-option>
</answer>

<post_analysis>
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