Question

Given: m || n and p is a transversal

Prove: mAngle2 = mAngle7

Horizontal and parallel lines m and n are cut by transversal p. On line m where it intersects line p, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line n where it intersects line p, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, 8, 7.
What is the missing reason in the proof?

Statement Reason
1. m || n and p is a transversal 1. given
2. ∠2 ≅ ∠3 2. ver. ∠s theorem
3. m∠2 = m∠3 3. def. of congruent
4. ∠3 ≅ ∠7 4. corr. ∠s theorem
5. m∠3 = m∠7 5. def. of congruent
6. m∠2 = m∠7 6. ?
corresponding angles theorem
alternate interior angles theorem
transitive property
subtraction property

Answer 1

3RD option

Explanation:

Answer 2

Option 3: transitive property

Explanation:

The previous statements are

2. ∠2 ≅ ∠3 ⇒ 2. ver. ∠s theorem

And

5. m∠3 = m∠7 ⇒ 5. def. of congruent

So, The previous proved statement to make use of the transitive property reason or proof

∴ 6. m∠2 = m∠7 ⇒ 6. transitive property

Note: the transitive property states that: If a = b and b = c, then a = c.