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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
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Take Note! These are two different rays!
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Name a ray in two ways.
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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?
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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?
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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?
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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
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ACUTE ANGLEACUTE ANGLE: An angle whose measure is less
than 90o
95o
50o
40o
30o
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ACUTE ANGLEACUTE ANGLE: An angle whose measure is less
than 90o
60o
Is the angle formed by 2 segments
acute?
95o
50o
40o
30o
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RIGHT ANGLERIGHT ANGLE: An angle whose measure is
90o
2 intersecting lines can form
angles.
90o
90o
40o
75o
126o
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OBTUSE ANGLEOBTUSE ANGLE: An angle whose measure is greater than 90o
95o
155o
60o
40o
130o
30o
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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.
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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.
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PARALLEL LINESPARALLEL LINES: Two coplanar lines that do not intersect.
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COMPLEMENTARY ANGLESCOMPLEMENTARY ANGLES: Two angles whose measures have the sum of 90o.
Pairs of Complementary
Angles
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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
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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
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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
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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
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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
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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
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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