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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

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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 Sign SUS -> 女 @ #3 $ % & 4 7 8. W e r y u i S d f j k
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.
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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