chapter 3 review. skew lines are noncoplanar lines that are neither parallel nor intersecting. f g
TRANSCRIPT
Parallel planes are planes that do not intersect
H
E
A
D
F
G
C
B
Pplane HEFG ????plane ADBC
Pplane HEDA ????plane GFBC
Pplane HGBA ????plane EFCD
A transversal is a line that intersects two or more coplanar lines in a different point.
m
k
t
NOTE: t is the transversal of line m and k
Classify the following angle pairs:
1 2
8 7
9 10
16 15
11 12
13 14
3 4
6 5
<10 and <13
<8 and <6
<15 and <14
<7 and <6
<15 and <11
<4 and <16
<10 and <11
AI
CA
CA
SSI
AI
Not related
SSI
PostulateIf two parallel lines are cut by a
transversal, then corresponding angles are congruent.
∠1≅ ∠31 2
8 7
3 4
6 5∠8 ≅ ∠6∠2 ≅ ∠4
∠7 ≅ ∠5
TheoremIf two parallel lines are cut by a
transversal, then alternate interior angles are congruent.
∠2 ≅ ∠61 2
8 7
3 4
6 5∠7 ≅ ∠3
TheoremIf two parallel lines are cut by a
transversal, then same side interior angles are supplementary.
∠2 +∠3 =1801 2
8 7
3 4
6 5∠7 +∠6 =180
TheoremIf a transversal is perpendicular
to one of the two parallel lines, then it is perpendicular to the other one also.
1 2
8 7
3 4
6 5
Theorem
Two lines parallel to a third line are parallel to each other.
m n p
m PnIf and n Pp
THEN
m Pp
Corollary If two angles of one triangle are
congruent to two angles of another triangle, then the third angles are congruent.
Exterior Angle Theorem
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.
A regular polygon is both equiangular and equilateral
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The sum of the measures of the angles of a convex polygon is
(n-2)180
Where n is the number of sides.
EXAMPLE: Find the sum of the measures of the angles of a nonagon.
(9-2)180
(7)180
1260
The measure of each interior angle of an equiangular polygon is
Where n is the number of sides
(n−2)180n
Find the measure of each interior angle of a regular octagon.
(8−2)1808
=(6)180
8=1080
8=135