Question

given lines ( l ) and ( m ) cut by transversal ( t ), alternate exterior angles ( angle 1 cong angle 8 ). prove ( l parallel m ).

statements
1.

1. ( angle 5 cong angle 8 )

3.

1. ( l parallel m )

reasons
1.
2.
3.

1. converse of the corresponding angles postulate

a. lines ( l ) and ( m ) cut by transversal, ( t ), alternate exterior angles ( angle 1 cong angle 8 )
b. ( angle 1 cong angle 5 )
c. transitive property of congruence
d. alternate interior angles theoreme. ( m angle 5 + m angle 8 = 180 ^ { circ } )
f. given
g. vertical angles theorem

Explanation:

Step1: State the given information

Lines \( l \) and \( m \) are cut by transversal \( t \), and \( \angle1\cong\angle8 \) (Given).

Step2: Use the Vertical Angles Theorem

\( \angle5\cong\angle8 \) (Vertical Angles Theorem).

Step3: Apply the Transitive Property of Congruence

Since \( \angle1\cong\angle8 \) (Given) and \( \angle5\cong\angle8 \) (Vertical Angles Theorem), then \( \angle1\cong\angle5 \) (Transitive Property of Congruence).

Step4: Use the Converse of the Corresponding Angles Postulate

If \( \angle1\cong\angle5 \), then \( l\parallel m \) (Converse of the Corresponding Angles Postulate).

Answer:

1. \( \angle1\cong\angle8 \), Given
2. \( \angle5\cong\angle8 \), Vertical Angles Theorem
3. \( \angle1\cong\angle5 \), Transitive Property of Congruence
4. \( l\parallel m \), Converse of the Corresponding Angles Postulate