Question

question 1 - 2
a proof is shown.
given: ( a parallel b ); and ( m ) is the transversal.
prove: ( angle 3 cong angle 5 )
statements

1. lines ( a ) and ( b ) are parallel with transversal ( m ).
2. ( angle 1 cong angle 5 )
3. ( angle 3 cong angle 1 )
4. ( angle 3 cong angle 5 )

reasons

1. given
2. corresponding angles are congruent.
3. vertical angles are congruent.

4.

Explanation:

Step1: Use corresponding angles theorem

Since \(a\parallel b\) and \(m\) is the transversal, by the corresponding angles theorem, \(\angle1\cong\angle5\).

Step2: Use vertical angles property

Vertical angles are congruent. So, \(\angle3\cong\angle1\).

Step3: Use transitive property

If \(\angle1\cong\angle5\) and \(\angle3\cong\angle1\), then by the transitive property of congruence, \(\angle3\cong\angle5\).

Answer:

1. Given
2. Corresponding angles are congruent.
3. Vertical angles are congruent.
4. Transitive property.