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PARALLEL & PERPENDICULAR
LINES
Activity 7
PARALLEL & PERPENDICULAR LINES
Date Learning Target
9/23 Proofs, Part II
9/28 Parallel Lines & Angles
Page
#
34
36
PARALLEL & PERPENDICULAR LINES
Learning Task
I will make conjectures about angles and
parallel lines and prove theorems about
the angles.
PARALLEL & PERPENDICULAR LINES
Parallel Lines - lines in the same plane that do not intersect
PARALLEL & PERPENDICULAR LINES
Transversal - line that intersects two or
more coplanar lines in different points
a
b
n
m
ANGLE PAIRS
Corresponding Angles - nonadjacent angles that are on
the same side of the transversal and one angle is in the
exterior and one angle is in the interior
Alternate Interior Angles - pair of angles that are in the
interior but on opposite sides of the transversal
Same-Side Interior Angles - nonadjacent pair of angles
that are in the interior and on the same side of the
transversal
MORE ANGLE PAIRS
Alternate Exterior Angles - pair of angles that are in the
exterior but on opposite sides of the transversal
Same-Side Exterior Angles - nonadjacent pair of angles
that are in the exterior and on the same side of the
transversal
ANGLE PAIRS
Corresponding Angles
∠1 & ∠5
∠2 & ∠6
∠4 & ∠8
∠3 & ∠7
ANGLE PAIRS
Alternate Interior Angles
∠3 & ∠6
∠4 & ∠5
ANGLE PAIRS
Alternate Exterior Angles
∠1 & ∠8
∠2 & ∠7
ANGLE PAIRS
Same-Side Interior Angles
∠3 & ∠5
∠4 & ∠6
ANGLE PAIRS
Same-Side Exterior Angles
∠2 & ∠8
∠1 & ∠7
POSTULATES AND THEOREMS
Corresponding Angles Postulate - If two parallel lines are
cut by a transversal, then the corresponding angles are
congruent
Alternate Interior Angles Theorem - If two parallel lines are
cut by a transversal, then the alternate interior angles are
congruent
Same-Side Interior Angles Theorem - If two parallel lines
are cut by a transversal, then the same-side interior angles
are supplementary
POSTULATES AND THEOREMS
Alternate Exterior Angles Theorem - If two parallel lines
are cut by a transversal, then the alternate exterior angles
are congruent
Same-Side Exterior Angles Theorem - If two parallel lines
are cut by a transversal, then the same-side exterior
angles are supplementary
PARALLEL & PERPENDICULAR LINES
Date
9/23
9/28
9/30
Learning Target
Proofs, Part II
Parallel Lines & Angles
Proving lines Parallel
Page
#
34
36
38
PARALLEL & PERPENDICULAR LINES
Learning Task
I will develop theorems and postulates
to prove lines are parallel.
PARALLEL & PERPENDICULAR LINES
Warm-up, p. 38 - Quick Write (2 minutes)
Write the converse, inverse and contrapostive for
the following statement. Determine if each
statement is true or false.
“If it is Sunday in the fall, there is a NFL football game
being played.”
PROVING LINES PARALLEL
Converse of the Corresponding Angles Postulate - If the
corresponding angles are congruent when two lines are cut
by a transversal, then the two lines are parallel
Converse of the Alternate Interior Angles - If the alternate
interior angles are congruent when two lines are cut by a
transversal, then the two lines are parallel
Converse of the Same-Side Interior Angles Theorem - If the
same-side interior angles are supplementary when two lines
are cut by a transversal, then the two lines are parallel
PROVING LINES PARALLEL
Converse of the Alternate Exterior Angles - If the alternate
exterior angles are congruent when two lines are cut by a
transversal, then the two lines are parallel
Converse of the Same-Side Exterior Angles Theorem - If the
same-side exterior angles are supplementary when two
lines are cut by a transversal, then the two lines are parallel
PROVING LINES PARALLEL
Warm-up, p. 38
Find the value of
“x” such that
l!m
PROVING LINES PARALLEL
HOMEWORK
p. 87, problems: 7, 9, 10, 11, 13,
15, 18, 19, 22, 23
Due Wednesday
Quiz Tuesday
Bring Chromebook
PARALLEL & PERPENDICULAR LINES
Date
9/23
9/28
9/30
10/4
Learning Target
Proofs, Part II
Parallel Lines & Angles
Proving lines Parallel
Perpendicular Lines
Page
#
34
36
38
40
PARALLEL & PERPENDICULAR LINES
Learning Task
I will develop theorems related to
perpendicular lines.
PARALLEL & PERPENDICULAR LINES
Perpendicular Lines - two lines that intersect to
form right angles
Perpendicular Bisector - a line that intersects a
segment at its midpoint to form right angles
POSTULATES AND THEOREMS
Perpendicular Postulate - If given a line and a point not on the line,
then there is exactly one line through the point that is
perpendicular to the given line
Parallel Postulate - If given a line and point not on the line, then
there is exactly one line through the point that is parallel to the
given line
Perpendicular Transversal Theorem - If a transversal is
perpendicular to one of two parallel lines, then it is perpendicular
to the other line