Derek wrote the following paragraph proof for the Vertical Angles Theorem:
The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. Angle 1 is equal to angle 3 _____________________.
Which phrase completes the proof?
A. by construction using a straightedge
B. by the definition of a perpendicular bisector
C. by the subtraction property of equality
D. by the vertical angles theroem
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I'm thinking its D
You can't use the reason of the vertical angles theorem to prove the vertical angles theorem.
I don't agree with the earlier statements of this proof. There are statements missing.
The answer is C, but this is a very bad proof.
Here is a better proof:
Angles 1 and 4 are a linear pair, so they are supplementary.
Angles 3 and 4 are a linear pair, so they are supplementary.
The measures of angles 1 and 4 add to 180 by the definition of supplementary angles.
The measures of angles 3 and 4 add to 180 by the definition of supplementary angles.
The sum of the measures of angles 1 and 4 equals the sum of the measures of angles 3 and 4 by substitution.
m<1 = m<3 by the subtraction property of equality
how is it C
this looks close to the answer im not sure just wondering