Prove the following indirectly using two-column form:

Question

Given: BA ⊥ AN

NI ⊥ AN

Angle 2 ≇ angle 4

Prove: Angle 1 ≇ angle 3

Answer 1

Assume <1 = <3

m<1 + m<2 = m<NAB angle addition postulate

m<3 + m<4 = m<ANI

<NAB and <ANI are right angles perpendicular lines form right angles

m<NAB = m<ANI = 90 right angles are 90 degrees in measure

m<1 + m<2 = m<3 + m<4 transitive property

m<3 + m<2 = m<3 + m<4 substitution

m<2 = m<4 subtraction

contradiction to what is given, so m<1 does not equal m<3