The correct completion of Sylvie's proof is:
4. 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.
Use the image to answer the question.
An illustration shows a triangle with angles marked as 1, 2 and 3, clockwise beginning at the top angle. A line is drawn outside of the triangle, passing through the vertex with angle 3.
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∠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.
m∠1+m∠3+m∠2=180°
by the definition of a straight angle. Finally, m∠5+m∠3+m∠4=180°
by substitution.
answer with 1-4
1 answer
1 answer