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CHAPTER 3
By: Team 2
Mr. Larose
Block 1
3-1 Lines & Angles
• Lines:
– Parallel lines- coplanar lines that don’t intersect.
– Skew lines- non-coplanar lines that are not parallel
and do not intersect.
– Parallel Planes- are planes that do not intersect.
– Transversal- a line that intersects two or more
coplanar lines.
3-1 Lines & angles.
• Angles
– Alternate interior angles- are nonadjacent interior
angles that lie on opposite sides of the transversal.
– Same-side interior angles- interior angles that lie
on the same side of the transversal.
– Corresponding- are on the same side of the
transversal and are in corresponding positions.
– Alternate exterior angles- nonadjacent exterior
angles that are on opposite side of the transversal
• Blue- Parallel lines
• Red- Transversal
• -Alternate interior
angles
• -Same-side
interior angles
• -Corresponding
angles
• -Alternate exterior
angles
3-2 Properties of parallel lines
• If two parallel lines are cut by a transversal, then
– Corresponding angles, alternate interior angles,
and alternate exterior angles are congruent
– Same-side interior angles are supplementary
Which angles are congruent to
•
•
•
-(Corresponding)
-(Alternate Interior)
-(Vertical)
3-3 Proving lines parallel
• If two lines and a transversal form
– Congruent corresponding angles
– Congruent alternate interior angles
– Congruent alternate exterior angles or
– Supplementary same-side interior angles
Then the two lines ARE PARALLEL.
3-4 Parallel & Perpendicular lines
– Two lines parallel to the same line are parallel to
each other.
– In a plane, two lines perpendicular to the same
line are parallel.
– In a plane, if one line is perpendicular to one of
two lines parallel lines then it is perpendicular to
both parallel lines.
3-5 Parallel lines & Triangles
- The sum of the measures of the angles of a
triangle is 180.
- The measure of the each exterior angle of a
triangle equals the sum of the measures of its
two remote interior angles.
3-6 Constructing parallel &
Perpendicular lines
• You can use a compass and a straightedge to
construct
– A line parallel to a given line through a point not
on the line
– A line perpendicular to a given line through a
point on the line, or through a point not on the
line
3-7 Equations of lines in the
Coordinate plane
• Slope-Intercept form is y =mx + b where m is
the slope and b is the Y-intercept.
• Point-slope form is y- y1=m(x-x1) where m is
the slope and (x1,y1) is a point on the line.
3-8 Slopes of parallel and
Perpendicular lines
• Parallel lines have the same slope
• The product of the slopes of two
perpendicular lines is -1.