Given: m∠1 = m∠2
And points D,F, and E are colinear
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Prove: AB ⊥ ED
m∠1 = m∠2 Given
∠1 and ∠2 form a linear pair D,F, and E are colinear
and adjacent angles
which form a straight
line form a linear pair
∠1 is supplementary to ∠2 If two angles form a linear pair,
they are supplementary
m∠1 + m∠2 = 180° Supplementary angles have sum 180°
m∠1 + m∠1 = 180° A quantity may be substituted
for its equal
2(m∠1) = 180° Definition of like terms
m∠1 = 90° Halves of equal quantities are
equal
∠1 is a right angle Definition of a right angle is one
whose measure is 90°
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AB ⊥ ED Definition of perpendicular
lines.
Edwin