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1.5 glenco geometry.notebook
September 09, 2014
1.5 Angle Relationships
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1.5 glenco geometry.notebook
September 09, 2014
Pairs of Angles: Some pairs of angles are special because of how they are positioned in relationship to each other. .
Definition: adjacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no other common points.
1
2
.
2
1
.
Angles 1 and 2 are adjacent angles
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1.5 glenco geometry.notebook
September 09, 2014
Two angles are vertical angles if their sides form two pairs of opposite rays.
Two adjacent angles are a linear pair if their noncommon sides are opposite rays.
Note: For this class , you can assume from a diagram that two adjacent angles form a linear pair if the noncommon sides appear to lie on the same line.
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1.5 glenco geometry.notebook
September 09, 2014
Example:
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1.5 glenco geometry.notebook
September 09, 2014
Example:
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1.5 glenco geometry.notebook
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1.5 glenco geometry.notebook
September 09, 2014
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1.5 glenco geometry.notebook
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1.5 glenco geometry.notebook
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1.5 glenco geometry.notebook
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1.5 glenco geometry.notebook
September 09, 2014
Two angles are complementary angles if the sum of their measures is 90°.
Each angle is the complement of the other. Complementary angles can be
adjacent or nonadjacent.
Two angles are supplementary angles if the sum of their measures is 180°.
Each angle is the supplement of the other. Supplementary angles can be
adjacent or nonadjacent.
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1.5 glenco geometry.notebook
September 09, 2014
Example:
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1.5 glenco geometry.notebook
September 09, 2014
Example
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1.5 glenco geometry.notebook
September 09, 2014
Example(s)
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1.5 glenco geometry.notebook
September 09, 2014
perpendicular.
Perpendicular Lines: Lines, Segments, or rays that form right angles are Perpendicular Lines
­ Intersect to form four right angles
­Perpendicular lines intersect to form congruent adjacent angles
­Segments and rays can be perpendicular to lines or other line segments and rays
­ The right angle symbol in the figure indicates that the lines are perpendicular
Symbol: is read is perpendicular to
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1.5 glenco geometry.notebook
September 09, 2014
In the figure below, it appears the lines FG and JK are perpendicular. However, you cannot assume this is true unless you are given other information, such as the measure of angle FHJ = 90 degrees is given.
F
K
H
J
G
In geometry, figures are sketches used to depict a situation. They are not drawn to reflect total accuracy. There are certain relationships that you can assume to be true, but others you cannot.
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1.5 glenco geometry.notebook
September 09, 2014
Interpreting Diagrams
J
H
K
G
M
L
CANNOT ASSUME
CAN BE ASSUMED
All pts. are coplanar
G, H, and J are collinear
Rays HM, HL, HK, and GJ intersect at H
H is between G and J
L is in the interior of angle MHK
Angle GHM and angle MHL are adjacent angles
Angles GHL and angle LHJ are a linear pair
Angles JHK and KHG are supplementary
Perpendicular lines
Congruent Angles
Congruent Segments
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1.5 glenco geometry.notebook
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