Post on 30-Apr-2020
CCSS.Math.Content.HSG-CO.A.1, HSG-CO.D.121•
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1•5 Angle RelationshipsPairs of Angles
Some angle pairs are defined by their position in relationship to each other.• Adjacent angles are two angles that lie in the same plane and
have a common vertex and a common side, but no common interior points.
• A pair of adjacent angles with noncommon sides that are opposite rays is called a linear pair.
• Vertical angles are two nonadjacent angles formed by two intersecting lines.
Some angle pairs are defined by the relationship between their measures.• Complementary angles are two angles with measures that have
a sum of 90.• Supplementary angles are two angles with measures that have
a sum of 180.
Angles and Angle Pairs
Name an angle pair that satisfies each condition.
A
B
C
DE
F
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H
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a. two vertical angles∠ EFI and ∠GFH are nonadjacent angles formed by two intersecting lines. They are vertical angles.
b. two adjacent angles∠ABD and ∠DBE have a common vertex and a common side but no common interior points. They are adjacent angles.
c. two supplementary angles∠EFG and ∠GFH form a linear pair. The angles are supplementary.
d. two complementary anglesm∠CBD + m∠DBE = 90. These angles are complementary.
EXAMPLE
Program: FL MATH REPRINT Component: HANDBOOK1st Pass
Vendor: LASERWORDS Grade: Geometry
52 HotTopic 1
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Perpendicular Lines
Lines, rays, and segments that form right angles are perpendicular. The right angle symbol indicates that the lines are perpendicular.
In the figure, � �� AC is perpendicular to � �� BD , or � �� AC ⊥ � �� BD .
B
CD
A
Perpendicular Lines
Find x so that ⎯⎯ � ZD and
⎯⎯ � ZP are perpendicular.
Z
D
P
Q(9x + 5)°
(3x + 1)°
If ��� ZD ⊥
��� ZP , then m∠DZP = 90.
m∠DZQ + m∠QZP = m∠DZP Definition of adjacent angles.
(9x + 5) + (3x + 1) = 90 Substitution
12x + 6 = 90 Combine like terms.
12x + 6 - 6 = 90 - 6 Subtract 6 from each side.
12x = 84 Simplify.
12x _ 12 = 84 _ 12 Divide each side by 12.
x = 7 Simplify.
EXAMPLE
Angle Relationships 53
Program: FL MATH REPRINT Component: HANDBOOK2nd Pass
Vendor: LASERWORDS Grade: Geometry
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1•5
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Construct Perpendiculars
You can construct the perpendicular bisector of a line segment using a compass and a straightedge.
Construct Perpendiculars
Use a compass and straightedge to construct the perpendicular bisector of −−
XY .
Step 1: Given line segment XY, open the compass wider than half of XY. Put the tip of the compass on X and draw an arc that goes above and below the line segment.
Step 2: Without changing your compass setting, put the tip on Y and draw an arc that intersects the first arc at W and Z.
Step 3: Draw line WZ. � ��� WZ is the perpendicular bisector of −−
XY .
X Y
X Y
W
Z
X Y
W
Z
EXAMPLE
Program: FL MATH REPRINT Component: HANDBOOK1st Pass
Vendor: LASERWORDS Grade: Geometry
54 HotTopic 1
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1•5 ExercisesFor Exercises 1–3, use the figure. 1. Identify two obtuse vertical angles.
2. Identify two acute adjacent angles.
3. Identify an angle supplementary to ∠TNU.
4. Find the measures of two complementary angles if the difference in their measures is 18.
5. Find the value of x and y so that � �� NR ⊥ � ��� MQ .
6. Find m∠MSN.
7. m∠EBF = 3x + 10, m∠DBE = x, and
��� BD ⊥
��� BF . Find the value
of x.
8. If m∠EBF = 7y - 3 and m∠FBC = 3y + 3, find the value of y so that
��� BE ⊥
��� BC .
9. Find the value of y, m∠RPT, and m∠TPW.
10. Copy −−− MN . Then construct the
perpendicular bisector of −−− MN .
R S
NU
T
V
M
N
R
S Q
P
x°5x°
(9y + 18)°
B CA
DE
F
P
S
V
R
W
T(4y - 5)°
(2y + 5)°
M N
Program: FL MATH Component: HANDBOOKPDF Pass
Vendor: LASERWORDS Grade: Geometry
Angle Relationships 55
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