kaleem wanted to draw a triangle where the sides measured 5 cm, 8 cm, and 7 cm. how many unique triangles could khaleem draw that fit these dimensions?

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Question

kaleem wanted to draw a triangle where the sides measured 5 cm, 8 cm, and 7 cm. how many unique triangles could khaleem draw that fit these dimensions?

1
2
3
4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Geometric Inequalities" ], "new_concepts": [ "Triangle Congruence Theorems", "SSS Congruence" ], "current_concepts": [ "Geometric Inequalities", "Triangle Congruence Theorems", "SSS Congruence" ] } ## Verify the triangle inequality theorem $$ \begin{aligned} &5 + 7 = 12 > 8 \ &5 + 8 = 13 > 7 \ &7 + 8 = 15 > 5 \end{aligned} $$ ## Determine uniqueness using SSS congruence $$ \text{By Side-Side-Side (SSS) Congruence, any triangle with sides } 5\text{ cm}, 8\text{ cm}, \text{ and } 7\text{ cm is congruent.} $$ $$ \text{Number of unique triangles} = 1 $$

(A) 1

(B) 2

(C) 3

(D) 4

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

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Question

Explanation:

Verify the triangle inequality theorem

Determine uniqueness using SSS congruence

Answer: