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Synthesize construction techniques, the triangle inequality, and angle properties to master triangle geometry.
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Checklist of the chapter's main outcomes.
Mixed questions spanning all concepts.
Which of the following sets of side lengths can successfully form a triangle?
A multi-step problem evaluating possibility of construction.
Let the unknown angles be represented algebraically (e.g., ). Prove whether three angles can form a triangle, and determine the necessary angle measure for an equilateral triangle.
List the known angle values provided in the prompt for the scenario where two angles are 70°.
State the geometric rule that dictates the total sum of interior angles in a triangle.
Write two equations: one to find the third angle if two are 70°, and one for when all three angles are identical (letting them equal x).
Show the algebra used to solve for the missing variables.
State your final numerical answers and clearly answer whether a 70°-70°-70° triangle is possible.