SOLUTION: Given: Triangle ABC Prove: m<4= m<1 + m<2 Picture: A triangle with line, CD, connected to it. A is m<1, B is m<2, C is m<3, and m<4 are vertical angles to m<3

Algebra ->  Geometry-proofs -> SOLUTION: Given: Triangle ABC Prove: m<4= m<1 + m<2 Picture: A triangle with line, CD, connected to it. A is m<1, B is m<2, C is m<3, and m<4 are vertical angles to m<3      Log On


   

Question 257494: Given: Triangle ABC
Prove: m<4= m<1 + m<2
Picture: A triangle with line, CD, connected to it. A is m<1, B is m<2, C is m<3, and m<4 are vertical angles to m<3
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is also called the exterior triangle theorem. With angle 4 vertical to angle 3, you cannot prove
angle 4 = angle 1 + angle 2. For this to work, angle 4 must be supplementary to angle 3. Here is the proof for that.
STATEMENT 1: triangle ABC
REASON 1: given
STATEMENT 2: angle 1 + angle 2 + angle 3 = 180 degrees
REASON 2: definition of sum of angles of triangle
STATEMENT 3: angle 3 + angle 4 = 180
REASON 3: definition of supplementary angles
STATEMENT 4: angle 1 + angle 2 + angle 3 = angle 3 + angle 4
REASON 4: substitution [2,3]
STATEMENT 5: angle 1 + angle 2 = angle 4
REASON 5: subtraction property of equality