Question

given: $overrightarrow{ab}paralleloverrightarrow{cd}$, $angle eijcongangle gji$. prove: $angle jikcongangle ijl$. 17 what is the reason for the last step in the given proof? a. substitution property of equality b. linear pair theorem c. congruent supplements theorem d. transitive property of equality e. for parallel lines cut by a transversal, corresponding angles are congruent. reset next
statement\treason
$angle eijcongangle gji$\tgiven
$mangle eij = mangle gji$\tdefinition of congruent angles
$angle eij$ and $angle jik$ are supplementary\tlinear pair theorem
$mangle eij+mangle jik = 180^{circ}$\tdefinition of supplementary angles
$mangle gji+mangle jik = 180^{circ}$\tsubstitution property of equality
$angle gji$ and $angle jik$ are supplementary\tdefinition of supplementary angles
$angle gji$ and $angle ijl$ are supplementary\tlinear pair theorem
$angle jikcongangle ijl$\t

Explanation:

The Congruent Supplements Theorem states that if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. Here, since ∠GJI and ∠JIK are supplements and ∠GJI and ∠JL are supplements, and ∠GJI is common, we can conclude ∠JIK≅∠JL based on this theorem.

Answer:

C. Congruent Supplements Theorem