Transcript Final Exam Review Ch. 3

FINAL EXAM REVIEW
Chapter 3
Key Concepts
Chapter 3 Vocabulary
parallel
skew
transversal
corresponding <‘s
alternate interior <‘s
same-side interior <‘s
triangle
scalene Δ
isosceles Δ
equilateral Δ
exterior <
interior <
remote interior <
polygon
vertex
diagonal
inductive reasoning
Theorem

If two parallel planes are cut by a third plane,
then the lines of intersection are parallel.
j
k
j // k
Postulate

If two // lines are cut by a transversal, then
corresponding angles are congruent.
~
// Lines => corr. <‘s =
2
1
4
3
5
7
6
8
Example: <1 =~ <5
CONVERSE corr. <‘s~ = => // Lines
Theorem

If two // lines are cut by a transversal, then
alternate interior angles are congruent.
~
// Lines => alt int <‘s =
2
1
4
3
5
7
6
8
Example: <3 =~ <6
CONVERSE
alt int <‘s ~= => // Lines
Theorem

If two // lines are cut by a transversal, then same
side interior angles are supplementary.
// Lines => SS Int <‘s supp
2
1
4
3
5
7
6
8
Example: <4 is supp to <6
CONVERSE SS Int <‘s supp => // Lines
Theorem

If a transversal is perpendicular to one of
two parallel lines, then it is perpendicular
to the other line.
CONVERSE
In a plane two lines perpendicular to the same line are parallel.
3 More Quick Theorems
.
Theorem:
Through a point outside a line,
there is exactly one line parallel to the given
line.
Theorem:
Through a point outside a line,
there is exactly one line perpendicular
to the given line.
Theorem:
Two lines parallel to a third line are
parallel to each other.
.
5 Ways to Prove 2 Lines Parallel
~
1. Show that a pair of Corr. <‘s are =
2.
3.
Alt. Int. <‘s are~ =
S-S Int. <‘s are supp
4. Show that 2 lines are
5.
to a 3rd line
to a 3rd line
Theorem

The sum of the measures of the angles of
a triangle is 180.
B
m<1 + m<2 + M<3 = 180
2
1
A
3
C
Corollaries (Off-Shoots) of the Previous Theorem
1) If two angles of a triangle are congruent to two angles of
another triangle, then the third angles are congruent.
c
a
c
b
a
b
2) Each angle of an equilateral triangle has measure 60.
60
60
60
3) In a triangle, there can be at most one right angle or obtuse angle.
4) The acute angles of a right triangle are complementary.
a
<a and <b are complementary
c
b
Theorem

The measure of an exterior angle of a
triangle equals the sum of the measures
of the two remote interiors.
m<a = m<b + m<c
b
a
c
40 + 110 = 150
Example:
110
40
30
150
Theorem
The sum of the measures of the
interior angles of a convex polygon
with n sides is (n-2)180.
Example:
5 sides. 3 triangles.
Sum of angle measures is
(5-2)(180) = 3(180)
= 540
Theorem
The sum of the measures of the
exterior angles of any convex
polygon, one angle at each vertex, is
360.
Homework
► pg.
111 Chapter Review (skip 16)
► pg. 112 Chapter Test (skip 13)