Select the correct answer from each drop-down menu. In ΔABC, . Complete the proof showing that is parallel to . Statement Reason 1. given 2. 3. using common denominators 4. segment addition 5. Substitution Property of Equality 6. ∠ABC ≅ ∠DBE Reflexive Property of Congruence 7. SAS criterion for similarity 8. ∠BAC ≅ ∠BDE Corresponding angles of similar triangles are congruent. 9. If the corresponding angles formed by two lines intersected by a transversal are congruent, then the lines are parallel.

1. The correct options are 2 and 4.

2. The measure of angle 6 is 60°.

Step-by-step explanation:

1.

It is given that a∥b , and c is not parallel to a or b. So, we can not establish any relationship among the angles on the line a,b and  angles on the line c.

If a traversal line intersect two parallel line, then corresponding angles, alternate exterior angle and alternate interior angles are equal.

Therefore  correct options are 2 and 4.

2.

It is given that AB∥CD and m∠3=120°.

Statements                     Reasons

​ m∥nm∠1=120° ​                Given

∠5≅∠1                             Corresponding angles are equal

m∠5=m∠1                    Angle Congruence Postulate

m∠5=120°                    Substitution Property of Equality

m∠6+m∠5=180°             Supplementary angle property

m∠6+120°=180°            Substitution Property of Equality

m∠6=60° ​                    Subtraction Property of Equality

Therefore the measure of angle 6 is 60°.