Final answer:
The prove that ∠1 is congruent to ∠2, we can use the definition of a midpoint and the fact that AE is a segment bisector of LR. The proof involves showing that ΔAKE is congruent to ΔEKR.
Step-by-step explanation:
To prove that ∠1 is congruent to ∠2, we need to use the given information and the definitions of midpoint and segment bisector.
Statement a: K is the midpoint of AE.
Statement b: AE is a segment bisector of LR.
Based on the definition of a midpoint, we know that K divides AE into two congruent segments: AK and KE.
This means that AK ≅ KE.
Since AE is a segment bisector of LR, it intersects LR at a right angle, creating four congruent angles.
Therefore, ∠AKE is congruent to ∠EKR.
By the transitive property of congruence, we can conclude that ∠AKE is congruent to ∠EKR.
Since AK ≅ KE and ∠AKE ≅ ∠EKR, we can use the angle-side-angle (ASA) congruence criterion to prove that ΔAKE is congruent to ΔEKR.
Thus, ∠1 is congruent to ∠2.