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Warm Up
x
Given: b ∥ c, ∠1
and ∠2 are
supplementary
2
1
Find x. Explain your
reasoning. (No
proof required.)
70
a
b
c
Practice
Given: a ∥ b, ∠1
and ∠2 are
supplementary
Prove: ∠3 ≅ ∠4
3
a
b
1
2
4
c
Quick Review
Parallel Postulate: If there is a line and a point not on that line,
there there is exactly one line through the point and parallel to
the original line.
Perpendicular Postulate: If there is a line and a point not on that
line, there is exactly one line through the point and perpendicular
to the original line.
Theorem 3.1: If two lines intersect to form a linear pair of
congruent angles, then the lines are perpendicular.
Theorem 3.2: If two sides of two adjacent acute angles are
perpendicular, then the angles are complementary.
Theorem 3.3: If two lines are perpendicular, then they intersect
to form four right angles.
Quick Review
Corresponding Angles Postulate: If two parallel lines are cut by a
transversal, then corresponding angles are congruent.
Alternative Interior Angles Theorem: If two parallel lines are cut
by a transversal, then alternative interior angles are congruent.
Alternative Exterior Angles Theorem: If two parallel lines are cut
by a transversal, then alternative exterior angles are congruent.
Consecutive Interior Angles Theorem: If two parallel lines are cut
by a transversal, then consecutive interior angles are
supplementary.
Perpendicular Transversal Theorem: If a transversal is
perpendicular to one of two parallel lines, then it is perpendicular
to the other.
Quick Review
Corresponding Angles Converse: If two lines are cut by a
transversal so that corresponding angles are congruent, then the
lines are parallel.
Alternate Interior Angles Converse: If two lines are cut by a
transversal so that alternate interior angles are congruent, then
the lines are parallel.
Alternate Exterior Angles Converse: If two lines are cut by a
transversal so that alternate exterior angles are congruent, then
the lines are parallel.
Consecutive Interior Angles Converse: If two lines are cut by a
transversal so that consecutive interior angles are
supplementary, then the lines are parallel.
Quick Review
Theorem 3.11: If two lines are parallel to the same line, then they
are parallel to each other. (Transitivity of parallelism)
Theorem 3.12: In a plane, if two lines are perpendicular to the
same line, then they are parallel to each other.
Pseudo-Quiz
Please write a 2-column proof of the
following.
t
1
a
Given: ∠1 and ∠2 are a linear pair of
congruent angles.
∠3 is a right angle.
a∥c
b
Prove: b ∥ c
c
2
3