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

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

Question

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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Congruence", "Corresponding Parts" ], "new_concepts": [], "current_concepts": [ "Triangle Congruence", "Corresponding Parts" ] } ## 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 $$ \begin{aligned} 5x + 1 &= 11\ 5x &= 10\ x &= 2 \end{aligned} $$

(A) $x = 2$

(B) $x = \frac{1}{5}$

(C) $x = 11$

(D) $x = 5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence" ] }

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QUESTION IMAGE

Question

Explanation:

Identify corresponding parts of congruent triangles

Solve the linear equation for x

Answer: