Question

Complete the proof below. Given:K is the midpoint of AE; AE is a segment bisector of LR Prove: ∠1≅∠2 K is the midpoint of AE; AE is a segment bisector of LR Statements? Reasons?

A)Given: K is the midpoint of AE.
B)Given: AE is a segment bisector of LR.
C)Draw a line segment LR.
D)Label points A and E on segment LR.
E)Draw a line segment KE, connecting point K to point E.

Answer 1

To prove that ∠1 is congruent to ∠2, we can use the properties of a segment bisector and the fact that K is the midpoint of AE.

Step-by-step explanation:

To prove that ∠1 is congruent to ∠2, we can use the properties of a segment bisector and the fact that K is the midpoint of AE.

1. Given that K is the midpoint of AE, we can say that AK = KE and AE is divided into two congruent segments.
2. Since AE is a segment bisector of LR, it means that AL = LE and ER = RL.
3. By using the transitive property of equality, we can now conclude that AK = KE = AL = LE and thus, ∠1 is congruent to ∠2.