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2.1 Exploring Patterns

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2.1 Exploring Patterns

Undefined terms : point, line and plane.

Line – an infinite set of points that extends in two directions

symbol

Plane – named using one capital letter or using 4 points in the plane

B

T

D

A

C

Plane T or Plane ABCD

The line segment/segment AB consists of the endpoints A and B and all points on AB that lie between A and B.

Line segment AB or BA

The ray AB consists of the initial point A and all points on the line AB that lie on the same side of A as B lies. If C is between A and B, then CA and CB are opposite rays.

RayAB

Opposite rays CA and CB A C BPoints, segments, or rays that lie on the same line are collinear.

In the line above, the following are collinear:A,B,C ; AC, CB, AB ; AC, CB, BC

- The term betweenness in geometry implies collinearity. D A C B
- C is between A and B.
- D is not between A and B
- The “length” of segment AB is written AB.

An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The angle that consists of the rays AB and AC is denoted by <BAC, <CAB, or <A. The point A is the vertex of the angle.

The measure of <A is denoted by m<A. Angles are classified as acute, right, obtuse, and straight.

Right : m<A = 90o

Acute : 0o < m<A < 90o

Obtuse : 90o < m<A < 180o

Straight: m<A = 180o

Every nonstraight angle has an interior and an exterior.

Interior – is between the points that lie on each side of the angle

Exterior – outside the angle

Two angles are adjacent if they share a common vertex and side, but have no common interior points.

<ABC is adjacent to <CBD

Because:

they have a common side (ray CB)

they have a common vertex (point B)

T

T

D

E

T

A

True or False.

1) and are opposite rays.

2) and are the same segment.

3) is the same as

4) is the same as

5) Is the same as

6) Is the same as

7) <JCH and <HCF are adjacent angles.

8) <DAE and <CAB are adjacent angles.

J

C

F

B

F

H

G

T

T

T

F

Homework : pg 61, 17 to 24, 27 to 34