Question

1. complete the 2 - column proof or sketch your completed proof block. given: be bisects ∠abd; bd bisects ∠ebc. prove: ∠abe≅∠dbc statements reasons 1. 1. 2. 2. 3. 3. 4. 4.

Explanation:

Step1: State the angle - bisector definition for ∠ABD

Since BE bisects ∠ABD, then ∠ABE = ∠EBD (by the definition of an angle - bisector, which divides an angle into two congruent angles).

Step2: State the angle - bisector definition for ∠EBC

Since BD bisects ∠EBC, then ∠EBD=∠DBC (by the definition of an angle - bisector).

Step3: Use the transitive property

Because ∠ABE = ∠EBD and ∠EBD = ∠DBC, we can conclude that ∠ABE=∠DBC (by the transitive property of equality, which states that if a = b and b = c, then a = c).

Answer:

Statements	Reasons
2. ∠ABE = ∠EBD	2. Definition of angle - bisector
3. BD bisects ∠EBC	3. Given
4. ∠EBD = ∠DBC	4. Definition of angle - bisector
5. ∠ABE = ∠DBC	5. Transitive property of equality