Chapter 3 Review. Skew lines are noncoplanar lines that are neither parallel nor intersecting. F G.

Chapter 3 Review

Skew lines are noncoplanar lines that are neither parallel nor intersecting.

F

G

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

In a plane two lines perpendicular to the same line are parallel.

m

n

m Pn

t

Theorem

Two lines parallel to a third line are parallel to each other.

m n p

m PnIf and n Pp

THEN

m Pp

TYPES OF TRIANGLES – Classification by sides

Scalene – no sides congruent.

TYPES OF TRIANGLES – Classification by sides

Isosceles– At least two sides congruent.

TYPES OF TRIANGLES – Classification by sides

Equilateral – all sides are congruent.

TYPES OF TRIANGLES – Classification by

angles Acute – three acute angles.

TYPES OF TRIANGLES – Classification by

angles Obtuse – one obtuse angle.

TYPES OF TRIANGLES – Classification by

angles Right – one right angle

TYPES OF TRIANGLES – Classification by

angles Equiangular – all angles are congruent

THEOREM

The sum of the measures of the angles of a triangle is 180

Corollary If two angles of one triangle are

congruent to two angles of another triangle, then the third angles are congruent.

Corollary

Each angle of an equiangular triangle has measure of 60 degrees.

180÷3=60

Corollary In a triangle, there can be at most

one right angle or obtuse angle.

Corollary

The acute angles of a right triangle are complementary.

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

website

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

The sum of the measures of the exterior angles of a convex polygon (one at each vertex) is

360

The measure of each exterior angle of an equiangular polygon is

Where n is the number of sides

360

n

Find the measure of each exterior angle of a regular octagon.

360

8=45