in which figure is $\\angle 1$ congruent to $\\angle 2$?
in which figure is $\\angle 1$ congruent to $\\angle 2$?
Answer
Explanation:
Step1: Analyze Top - Left Figure
In the top - left figure, we have two non - parallel lines cut by a transversal. The angles ∠1 and ∠2 are formed by a transversal intersecting two non - parallel lines. For two angles formed by a transversal and two lines to be congruent, there should be some special relationship (like corresponding angles for parallel lines). Since the two lines are not parallel, ∠1 and ∠2 are not congruent.
Step2: Analyze Top - Right Figure
In the top - right figure, we have two parallel lines (the vertical lines with arrows) cut by a transversal (the slanting line). ∠1 and ∠2 are corresponding angles. By the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then corresponding angles are congruent. So in this figure, ∠1 and ∠2 are congruent.
Step3: Analyze Bottom - Left Figure
In the bottom - left figure, the two lines (the two slanting lines) are not parallel. The angles ∠1 and ∠2 are formed by a transversal, but since the lines are not parallel, there is no guarantee of congruence. The angles here do not satisfy the conditions for congruent angles formed by a transversal (like corresponding, alternate - interior etc. for parallel lines).
Step4: Analyze Bottom - Right Figure
In the bottom - right figure, the two lines (the two slanting lines) are not parallel. The angles ∠1 and ∠2 are formed by a transversal, but without the lines being parallel, the angles are not congruent. They do not meet the criteria for congruent angles formed by a transversal.