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

Transitive property

Step-by-step explanation:

Given:

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. ?

Note:

Transitive property states that: If a = b and b = c, then a = c.

Solve:

2. ∠2 ≅ ∠3  ⇒ 2. ver. ∠s theorem

5. m∠3 = m∠7 ⇒ 5. def. of congruent

These statement to make use of the transitive property reason or proof.

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

Hence, the answer is Transitive property.

~Lenvy!~

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.