Transcript Parallel and Perpendicular Lines

Parallel and Perpendicular Lines
By: Artie Cieply, Eugene Jacob Nicolls,
Joe Marine, Matt Reed
Key Vocab
• Transversal- A line that intersects two coplanar lines at two distinct points
Ex.
1 2
3 4
5 6
7 8
• Alternate Interior Angles- Angles 3 & 6 and 4 & 5 are alt. int. angles
• Corresponding Angles- Angles 1 & 5, 2 & 6, 3 & 7, and 4 & 8 are
corresponding angles
• Same-side Interior Angles- Angles 3 & 5 and 4 & 6 are same-side int. angles
• Alternate Exterior Angles- Angles 1 & 8 and 2 & 7 are alt. ex. Angles
• Same-side Exterior Angles- Angles 1 & 7 and 2 & 8 are same-side ex. Angles
If two coplanar lines are parallel and a transversal splits them,
then alt. int. angles, corresponding angles, and alt. ex.angles are
congruent and same-side int. & ex. are supplementary.
More Key Terms
• Equiangular Triangle- A triangle with all angles congruent.
• Equilateral Triangle- A triangle with all sides congruent.
• Exterior Angle of a Polygon- An angle formed by a side and an extension of
an adjacent side.
• Flow Proof- A proof where arrows show the logical connections between
the statements.
• Isosceles Triangle- A triangle with two congruent sides.
• Polygon- A closed figure with at least three sides that are segments.
• Regular Polygon- An equilateral and equiangular regular polygon.
• Remote Interior Angles- The non adjacent angles of the exterior angle of a
triangle. Added together, the two angles equal the exterior angle.
• Scalene Triangle- A triangle with no sides congruent.
Properties of Parallel Lines
A transversal is a line that intersects
t
2 coplanar lines at 2 distinct
points. The diagram shows the 8
angles formed by a transversal t
and 2 lines l and m.
l
m
Pairs of the 8 angles have special names as suggested by their positions.
<1 and <2 are alternate interior angles.
<1 and <4 are same-side interior angles.
<1 and <7 are corresponding angles.
1 3
1 3
4
2
1 3
4 2
4
7
2
8
Proving Parallel Lines
You can prove two lines are parallel if a transversal splits them and the
corresponding angles, alternate interior angles, or alternate exterior
angles are congruent. Also, if the same-side interior or exterior angles
are supplementary.
Parallel and Perpendicular Lines
• Parallel lines lie in the same plane and do not
intersect.
• Perpendicular lines are intersecting lines that
form right angles
Parallel Lines and Triangle Angle Sum
Theorem
• The sum of the measures of the angles of a
triangle is 180 ̊
• M<A + M<B + M<C = 180 ̊̊
Polygon Angle Sum Theorems
• Sum of Interior Angles: (n-2)(180) n being the
number of sides the polygon has
• Sum of Exterior Angles: 360 ̊
Lines in the Coordinate Plane
• The slope-intercept form of a linear equation is y=mx+b, where m is
the slope of the line and b is the y-intercept.
Slopes of Parallel and Perpendicular
Lines
• Parallel lines slopes are equal.
• Perpendicular lines slopes are negative
reciprocals.
• Intersecting lines are crossing but have
different slopes.
Constructing Parallel and
Perpendicular Lines
Given: line l and point N not on l
.n
l
Step I:Label 2 points H and J on l.
N
Draw HN.
H
J
l
Step II: Construct 1 with a vertex at N so that 1
NHJ and the 2 angles
are corresponding angles. Label the line you just constructed M.
m
l
m
l
N 1
H
J