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How do you prove corresponding angles are equal?

1 Answer
Dec 24, 2015

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Suppose you have two parallel lines cut by a transversal.

Due to the straight angle (linear pair) theorem, we know that

#{(mangle2+mangle3=180˚),(mangle5+mangle6=180˚):}#

Thought the transitive property, we can say that

#mangle2+mangle3=mangle5+mangle6color(white)(xxxx)# (1)

Though the alternate interior angles theorem, we know that

#mangle3=mangle5#

Use substitution in (1):

#mangle2+mangle3=mangle3+mangle6#

Subtract #mangle3# from both sides of the equation

#mangle2=mangle6#

#thereforeangle2congangle6#

Thus #angle2# and #angle6# are corresponding angles and have proven to be congruent.