Sylvie has started a proof of the Triangle Angle Sum Theorem. Which answer choice correctly completes her proof? Sylvie's Proof: Given the diagram shown, ∠1≅∠5 ; ∠2≅∠4 because alternate interior angles are congruent when lines are parallel. Then, I know that m∠1=m∠5 ; m∠2=m∠4 because congruent angles have equal measures. (1 point) Responses m∠2+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by substitution. m angle 2 plus m angle 3 plus m angle 4 equals 180 degrees by the definition of a straight angle. Finally, m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees by substitution. m∠5+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by substitution. m angle 5 plus m angle 3 plus m angle 4 equals 180 degrees by the definition of a straight angle. Finally, m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees by substitution. m∠1+m∠3+m∠2=180° by the definition of a straight angle. Finally, m∠5+m∠3+m∠4=180° by substitution. m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees by the definition of a straight angle. Finally, m angle 5 plus m angle 3 plus m angle 4 equals 180 degrees by substitution. m∠5+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by the Triangle Angle Sum Theorem. m angle 5 plus m angle 3 plus m angle 4 equals 180 degrees by the definition of a straight angle. Finally, m angle 1 plus m angle 3 plus m angle 2 equals 180 degrees by the Triangle Angle Sum Theorem.
1 answer
The correct completion for Sylvie's proof is:
m∠5+m∠3+m∠4=180° by the definition of a straight angle. Finally, m∠1+m∠3+m∠2=180° by substitution.
This completion uses the concept of the straight angle to establish that the sum of angles at a point (or along a straight line) is 180°, and then uses substitution to derive that the sum of the angles in the triangle is also 180°, thus completing the proof of the Triangle Angle Sum Theorem.
