Triangle Proofs Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items

Question
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.

Fill in the blanks to complete the proof that m∠1+m∠3+m∠2=180°
given the diagram.

(2 points)
Given the diagram shown, ∠
≅∠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. m∠
+m∠3+m∠4=180°
by the definition of a straight angle. Finally, m∠1+m∠3+m∠
=180°
by substitution.
Remaining Attempts : 1

Answer 1

To complete the proof that m∠1 + m∠3 + m∠2 = 180° using the information given in the triangle with angles 1, 2, and 3, here’s how you can fill in the blanks:

Given the diagram shown, ∠3 ≅ ∠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. m∠1 + m∠5 + m∠4 = 180° by the definition of a straight angle. Finally, m∠1 + m∠3 + m∠2 = 180° by substitution.

So the completed proof would be:

Given the diagram shown, ∠3 ≅ ∠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. m∠1 + m∠5 + m∠4 = 180° by the definition of a straight angle. Finally, m∠1 + m∠3 + m∠2 = 180° by substitution.