In the proof below, what statement is needed in line 2 complete the prool? Given: AXYZ Prove: m/1 + m22+ m23 = 180 %3D W 4/1 2 3 Statements Reasons 1. Through point X, draw XW so that XW 1. Through any point not on a line, there is exactly one line parallel to the given line. 2. 2. Angle Addition Postulate 3. 22 24; 25 2 23 3. If parallel lines are cut by a transversal, then alternate interior angles are congruent. 4.m/2 m24; m25 4. Definition of congruent angles. m23 !! !! 5. m/1 +mz2+ m/3= 180 5. Substitution Property
In the proof below, what statement is needed in line 2 complete the prool? Given: AXYZ Prove: m/1 + m22+ m23 = 180 %3D W 4/1 2 3 Statements Reasons 1. Through point X, draw XW so that XW 1. Through any point not on a line, there is exactly one line parallel to the given line. 2. 2. Angle Addition Postulate 3. 22 24; 25 2 23 3. If parallel lines are cut by a transversal, then alternate interior angles are congruent. 4.m/2 m24; m25 4. Definition of congruent angles. m23 !! !! 5. m/1 +mz2+ m/3= 180 5. Substitution Property
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
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![In the proof below, what statement is needed in line 2 complete the proof?
Given: AXY Z
Prove: m/1+m22+ m23 = 180*
W
4/1
2
Y
3
Statements
Reasons
1. Through any point not on a line, there is exactly one line parallel to the given line.
1. Through point X, draw XW so that XW || YŹ
2.
2. Angle Addition Postulate
3. 22 4; 25 23
3. If parallel lines are cut by a transversal, then alternate interior angles are congruent.
4.m/2 = m4; m/5 = m23
4. Definition of congruent angles.
5. m/1+m22 + m/3
180
5. Substitution Property
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Transcribed Image Text:In the proof below, what statement is needed in line 2 complete the proof?
Given: AXY Z
Prove: m/1+m22+ m23 = 180*
W
4/1
2
Y
3
Statements
Reasons
1. Through any point not on a line, there is exactly one line parallel to the given line.
1. Through point X, draw XW so that XW || YŹ
2.
2. Angle Addition Postulate
3. 22 4; 25 23
3. If parallel lines are cut by a transversal, then alternate interior angles are congruent.
4.m/2 = m4; m/5 = m23
4. Definition of congruent angles.
5. m/1+m22 + m/3
180
5. Substitution Property
Sign
SUS
->
女
@
#3
$
%
&
4
7
8.
W
e
r
y
u
i
S
d
f
j
k
![O m/1+ mZ2 = m/3
O m/4 + m/1+m/5 = 180°
%3D
O m24 + m/5
= mZ1
m22+ m23 = 90°
->
#3
2$
%.
2
6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64c824e4-0121-439e-8aec-337ce9a5a2c1%2Ff6030a93-ed63-4ff6-9e60-548b445a5280%2Fijl2peo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:O m/1+ mZ2 = m/3
O m/4 + m/1+m/5 = 180°
%3D
O m24 + m/5
= mZ1
m22+ m23 = 90°
->
#3
2$
%.
2
6.
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