RAYRAY: Defined as …Ray AB is part of line AB that contains Point A and all the points on line AB that are on the same side of point A as point B. Ray AB has an endpoint of A;

A

B

Ray AB

Take Note! These are two different rays!

Name a ray in two ways.

ANGLEANGLE: Two rays that share a common endpoint, provided that the two rays do not lie on the same line. The common endpoint of the two rays that make an angle is the vertex of the angle. The two rays are called the sides of the angle.

Vertex AASide

Side How do we name

angles?

MEASURE OF AN ANGLEMEASURE OF AN ANGLE: The smallest amount of rotation for a

ray to move from the overlapping position to the final position

In DEGREES

115o28.6o

How do write an angle’s

measure in symbol

form?

CONGRUENTCONGRUENT: Two geometric figures are congruent if and only if they are identical in shape and size.

40o

40o

Are these congruent

even if they point to different

directions?

CONGRUENT ANGLESCONGRUENT ANGLES: Two angles are congruent angles if and only if they have the same measure.

40o

40o

ABC XYZ m ABC m XYZ

ACUTE ANGLEACUTE ANGLE: An angle whose measure is less

than 90o

95o

50o

40o

30o

ACUTE ANGLEACUTE ANGLE: An angle whose measure is less

than 90o

60o

Is the angle formed by 2 segments

acute?

95o

50o

40o

30o

RIGHT ANGLERIGHT ANGLE: An angle whose measure is

90o

2 intersecting lines can form

angles.

90o

90o

40o

75o

126o

OBTUSE ANGLEOBTUSE ANGLE: An angle whose measure is greater than 90o

95o

155o

60o

40o

130o

30o

ANGLE BISECTORANGLE BISECTOR: A ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure.

What ray bisects Angle ABC? 60o

60o

A

BC

D

ERay BD.

ANGLE BISECTORANGLE BISECTOR: A ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure.

60o

60o

A

BC

DIs the green ray an angle bisector

of Angle ABE?

ENo. The ray does

not share the vertex of angle

ABE.

PARALLEL LINESPARALLEL LINES: Two coplanar lines that do not intersect.

COMPLEMENTARY ANGLESCOMPLEMENTARY ANGLES: Two angles whose measures have the sum of 90o.

Pairs of Complementary

Angles

VERTICAL ANGLESVERTICAL ANGLES: If Line AB and Line CD intersect at point P so that point P is between points A and B and also between points C and D, then APC and BPD are a pair of vertical angles. Angles APD and BPC are also a pair of vertical angles.

ABABBBBBBBBBBBBB B

A

B

D

C

P

Common vertex

ABABBBBBBBBBBBBB B

G

R

H

S

T

W P

X

Pairs of Vertical Angles:

G and R; W and P; X and T; S and H

Are these pairs of Vertical Angles:

B and F?Z and K? J and A?

B

F

ZA

KJ

PERPENDICULAR LINESPERPENDICULAR LINES: Two lines that intersect to form a right angle.

A right angle is an angle whose measure is 90

degrees. Therefore,

perpendicular lines form angles

of 90 degree measures.

Line J

Line B

PERPENDICULAR LINESPERPENDICULAR LINES: Two lines that intersect to form a right angle.

Are intersecting lines always

perpendicular?

No. Can we call the green segments as perpendicular

segments?

90o

SUPPLEMENTARY ANGLESSUPPLEMENTARY ANGLES: Two angles whose measures have the sum of 180o.

Pairs of Supplementary

Angles

A M

D G

95o

70o 110o

85o

30o 150o

LINEAR PAIR OF ANGLESLINEAR PAIR OF ANGLES: If X, Y, and Z are consecutive collinear points and W is a point not on Line XZ, then XYW and WYZ form a linear pair of angles.

ABABBBBBBBBBBBBB B

X Y Z

W

Collinear points

LINEAR PAIR OF ANGLESLINEAR PAIR OF ANGLES: 2 angles form a linear pair if they share the same vertex, share same sides, and whose non-shared sides form a line.

ABABBBBBBBBBBBBB B

Shared sides

Non-Shared sides

Non-Shared sides

Common Vertex

G H