Question

Given: Lines y and z are parallel, and ABC forms a triangle.

Prove: m∠5 + m∠2 + m∠6 = 180°

Lines y and z are parallel. Triangle A B C sits between the 2 lines with point A on line y and points C and B on line z. Angle C A B is 2. Its exterior angle to the left is 1 and its exterior angle to the right is 3. Angle A B C is 6 and its exterior angle to the right is 7. Angle B C A is 5 and its exterior angle to the left is 4.


Statements

Reasons
1. ABC is a triangle 1. given
2. y ∥ z 2. given
3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ?
4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅
5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate
6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle
7. m∠5 + m∠2 + m∠6 = 180° 7. substitution
Which could be the missing reason in Step 3?

alternate interior angles are congruent
alternate exterior angles are congruent
vertical angles are congruent
corresponding angles are congruent

Answer 1

corresponding angles are congruent

Reason: AC and AB are transversals of the parallel lines y and z, so the angles at A correspond to the angles at C and B respectively, giving ∠1 ≅ ∠5 and ∠3 ≅ ∠6.