Question

use the diagram below for # 12. 12. determine which lines, if any, can be proved parallel given the angle relationship. give the converse to justify your answer. angle relationship parallel lines converse a. ∠8≅∠19 b. ∠13≅∠15 c. m∠14 + m∠18 = 180° d. m∠6 + m∠19 = 180° e. ∠4≅∠23 a. corresponding angles converse b. alternate interior angles converse c. alternate exterior angles converse d. consecutive interior angles converse

Explanation:

Step1: Identify angle - type for a

$\angle8$ and $\angle19$ are alternate exterior angles. If alternate exterior angles are congruent, lines are parallel.

Step2: Identify angle - type for b

$\angle13$ and $\angle15$ are alternate interior angles. If alternate interior angles are congruent, lines are parallel.

Step3: Identify angle - type for c

$\angle14$ and $\angle18$ are consecutive interior angles. If consecutive interior angles are supplementary, lines are parallel.

Step4: Identify angle - type for d

$\angle6$ and $\angle19$ are consecutive interior angles. If consecutive interior angles are supplementary, lines are parallel.

Step5: Identify angle - type for e

$\angle4$ and $\angle23$ are corresponding angles. If corresponding angles are congruent, lines are parallel.

Answer:

Angle Relationship	Parallel Lines	Converse
b. $\angle13\cong\angle15$	$j\parallel k$	B. Alternate Interior Angles Converse
c. $m\angle14 + m\angle18=180^{\circ}$	$j\parallel k$	D. Consecutive Interior Angles Converse
d. $m\angle6 + m\angle19 = 180^{\circ}$	$l\parallel m$	D. Consecutive Interior Angles Converse
e. $\angle4\cong\angle23$	$l\parallel n$	A. Corresponding Angles Converse