Question

1. the figure shows the plans for the roof of a house and its garage. the front rafters of the garage and house are to be parallel. what must be true about ∠1 and ∠2 for the rafters to be parallel? f a pair of congruent corresponding angles g a pair of congruent alternate interior angles h a pair of congruent alternate exterior angles j a pair of supplementary same - side interior angles

Explanation:

To determine the relationship between \(\angle 1\) and \(\angle 2\) for the rafters (lines) to be parallel, we use the Corresponding Angles Postulate. Corresponding angles are in the same position relative to the transversal (the base line) and the two lines (rafters). If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. \(\angle 1\) and \(\angle 2\) are corresponding angles here. Option F states "A pair of congruent corresponding angles", which matches the postulate. Option G refers to alternate interior angles (different position), H to alternate exterior (wrong position), and J to same - side interior (supplementary for parallel, but not the case here as \(\angle 1\) and \(\angle 2\) are corresponding).

Answer:

F. A pair of congruent corresponding angles