Answer:

Statements Reasons

1. E is between D and F Given

2. D, E, and F are collinear points, and E is on DF Definition of between

3. DE + EF = DF Segment Addition Postulate

4. DE = DF ? EF Subtraction property of equality

2. If ?BD divides ?ABC into two angles, ?ABD and ?DBC, then m?ABC = m?ABC - m?DBC.

?BD divides ?ABC into two angles, ?ABD and ?DBC.

Given: ?BD divides ?ABC into two angles, ?ABD and ?DBC

Prove: m?ABD = m?ABC - m?DBC.

Statements Reasons

1. ?BD divides ?ABC into two angles, ?ABD and ?DBC Given

2. m?ABD + m?DBC = m?ABC Angle Addition Postulate

3. m?ABD = m?ABC - m?DBC Subtraction property of equality

3. The angle bisector of an angle is unique.

?ABC with two angle bisectors: ?BD and ?BE.

Given: ?ABC with two angle bisectors: ?BD and ?BE.

Prove: m?DBC = 0.

Step-by-step explanation:

Yes

Theorem 8.3: If two angles are complementary to the same angle, then these two angles are congruent.

?A and ?B are complementary, and ?C and ?B are complementary.