Download Vertical Angles

Vertical Angles
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Find the measures of angles formed by intersecting lines.
VOGABULARY
Vertical angles
Linear pair
Vertical An$les and Linea,r Pairs
Determi4e whether the labeled angles are vertical anfles, a linear
pair, or neither.
Solution
a. 11, and 12
are
because they are adjacent and
their noncommon sides are on the same line.
l3
c. l5
b.
and
14 are
and
l6are
because they are not adjacent
and their sides are formed by two intersecting Iines.
38
I
Geometry, Concepts and Skills
Notetaklng.Gulde Chapter 2
POSTULAf,E
7:
LINEAR PAIR POSTUIATE
Words lf two angles form a linear pair, then
they are supplementary.
Symbols
ml.l, +'ml2
THEOREM
:
2.3: VERTrcAL ANGLES
_
Symbols, 11,
= 13 unA Z
THEOREM
Words Vertieal angles are
Use
tfie
'''
--
Z.-
Lineiar Pafu Postulate
Find the measure of IRSU.
Solution
IRSU and IUST are
. By the Linear Pair Postulate,
they are
mIRSU:
180o
Use
-
mIUST
:
tfie Vertical An{lesilheorem
Find the measure ol
ICED.
Solution
IAEB and ICED are
/
'
Theorem,J=
nICED : mIAEB :
Lesson
'.
2.4
angles. By the Vertical Angles
Geometry Concefis and Skllls NotetaktngGulde
Find Anfle Measures
Find m11,,
ml2,
and
ml3.
Solution
ml2:
Use the VerticalAngles Theorem.
mlL: 180o ml3 : ml
Use the
linear Pair Postulate.
Use the VerticalAngles Theorem.
Use Algebra with Vertical Angles
Find the value of y.
Solution
Because the two expressions are measures of vertical angles, you
can write the following equation.
(4y'
42)o
:
Vertical Angles Theorem
Simplify.
Divide each side by
Simplify.
-
Follow.Up Check your answer for Example 5.
substitute your value for y in the original equation to determine
whether it is a solution.
Geometry, Concepts and Skllls Notetaklng Guide
I
.
Chapter 2
O
Cnec?rylotnt Find ml7-,
ml2,
and
ml3.
7,.
Find the value of the variable.
Lesson
2.4
Geometry, Goncefls and Skllls Notetaklng
Gulde
4L