how to prove that a pair of corresponding angles are equal without using alternate interior angles conceot
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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
{
m
∠
2
+
m
∠
3
=
180
˚
m
∠
5
+
m
∠
6
=
180
˚
Thought the transitive property, we can say that
m
∠
2
+
m
∠
3
=
m
∠
5
+
m
∠
6
×
×
(1)
Though the alternate interior angles theorem, we know that
m
∠
3
=
m
∠
5
Use substitution in (1):
m
∠
2
+
m
∠
3
=
m
∠
3
+
m
∠
6
Subtract
m
∠
3
from both sides of the equation
m
∠
2
=
m
∠
6
∴
∠
2
≅
∠
6
Thus
∠
2
and
∠
6
are corresponding angles and have proven to be congruent.
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