Two-column proofs

[Geometrydude147]

I am totally lost and have a test on monday
Could anyone help me with 2 column proofs??

1. GIVEN: AB=BC PROVE: 1/2AC=BC

Statements Reasons
a. AB=BC Given
b. AC=AB+BC Symmetric
c. AB+AB=AC Substitution
d. AC=2BC Division
e. 1/2AC=BC Multiplication

Not sure if the reasons are correct!

2. GIVEN: Angle 1 and angle 3 are a linear pair; angle 2 and angle 3 are a linear pair
PROVE: m angle 1 = m angle 2, without using the vertical angle theorem

Statements Reasons
a. Angle 1 and angle 3 are supplementary Definition of supplementary angles
Angle 2 and angle 3 are supplementary
b. Angle 1 is congruent Angle 2 Substitution
c. Angle 1 equals angle 2 Definition of congruent angles

Again, not sure if correct.

Please give feedback!

 

[Mrspi]

I am totally lost and have a test on monday
Could anyone help me with 2 column proofs??

1. GIVEN: AB=BC PROVE: 1/2AC=BC

Statements Reasons
a. AB=BC Given
b. AC=AB+BC Symmetric
c. AB+AB=AC Substitution
d. AC=2BC Division
e. 1/2AC=BC Multiplication

Not sure if the reasons are correct!

I'm pretty sure that at least SOME of them are incorrect...but I'm not going to make any assumptions about what kind of diagram was provided with this exercise...I'm very sure there WAS one.

2. GIVEN: Angle 1 and angle 3 are a linear pair; angle 2 and angle 3 are a linear pair
PROVE: m angle 1 = m angle 2, without using the vertical angle theorem

Statements Reasons
a. Angle 1 and angle 3 are supplementary Definition of supplementary angles
Angle 2 and angle 3 are supplementary
I think that angle 1 and angle 3 are supplementary, and angle 2 and angle 3 are supplementary because of what my book calls the "linear pair postulate." The definition of supplementary angles says that "two angles are supplementary if and only if the sum of their measures is 180 degrees." Nothing in the proof so far has said anything about angle measures.


b. Angle 1 is congruent Angle 2 Substitution No.....you can say that angle 3 is congruent to angle 3 because of the Reflexive Property of Congruence
c. Angle 1 equals angle 2 Definition of congruent anglesNo....you can say that angle 1 is congruent to angle 2 because two angles that are supplements of the same angle are congruent to each other. In order to use the Definition of Congruent Angles (which says that two angles are congruent if and only if their measures are the same) you would have to have shown that the two angles in question have equal measures

Again, not sure if correct.

Please give feedback!