日 Given: ON ML, LP PN, ZOPN Prove: OPN 2 MPL is a right angle. 7. N. M. Given: , ON ML, LP PN, and ZOPN ZL 2ZN by Vertical Angles Theorem M2OPN m/LPM ZLPM is a right angle; definition of right angles OPN and NPL OPN MPL is a right angle. 06 by substitution definition of right angles 06 and are right triangles Review progress Question 2 ,demmon onght angles m/LPM = 90 by substitution ZLPM is a right angle; definition of right angles OPN and NPL OPN MPL by SSS. %3D and are right triangles Given: ON ML, LP PN and ZOPN ZOPN LPLM M2OPN m/PLM MZOPN m/PLM= 90 by substitution ZPLM is a right angle; definition of right angles OPN MPL by SAS. is a right angle. by Vertical Angles Theorem ; definition of congruent angles 06 ; definition of right angles %3D Given: ON ML, LP PN, and ZOPN ZOPN ZLPM m/OPN m/LPM is a right angle. by Vertical Angles Theorem ; definition of congruent angles 06 = Nd07W by substitution ;definition of right angles ZLPM is a right angle; definition of right angles OPN and NPL and are right triangles OPN MPL by Hypotenuse-Leg Review progress Question 2

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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Question

given: on congruent ml, pl congruent pn

日
Given: ON ML, LP PN, ZOPN
Prove: OPN 2 MPL
is a right angle.
7.
N.
M.
Given: , ON ML, LP PN, and ZOPN
ZL 2ZN by Vertical Angles Theorem
M2OPN
m/LPM
ZLPM is a right angle; definition of right angles
OPN and NPL
OPN MPL
is a right angle.
06
by substitution
definition of right angles
06
and are right triangles
Review progress
Question 2
Transcribed Image Text:日 Given: ON ML, LP PN, ZOPN Prove: OPN 2 MPL is a right angle. 7. N. M. Given: , ON ML, LP PN, and ZOPN ZL 2ZN by Vertical Angles Theorem M2OPN m/LPM ZLPM is a right angle; definition of right angles OPN and NPL OPN MPL is a right angle. 06 by substitution definition of right angles 06 and are right triangles Review progress Question 2
,demmon onght angles
m/LPM = 90 by substitution
ZLPM is a right angle; definition of right angles
OPN and NPL
OPN MPL by SSS.
%3D
and are right triangles
Given: ON ML, LP PN and ZOPN
ZOPN LPLM
M2OPN m/PLM
MZOPN
m/PLM= 90 by substitution
ZPLM is a right angle; definition of right angles
OPN MPL by SAS.
is a right angle.
by Vertical Angles Theorem
; definition of congruent angles
06
; definition of right angles
%3D
Given: ON ML, LP PN, and ZOPN
ZOPN ZLPM
m/OPN m/LPM
is a right angle.
by Vertical Angles Theorem
; definition of congruent angles
06 = Nd07W
by substitution
;definition of right angles
ZLPM is a right angle; definition of right angles
OPN and NPL
and are right triangles
OPN MPL by Hypotenuse-Leg
Review progress
Question 2
Transcribed Image Text:,demmon onght angles m/LPM = 90 by substitution ZLPM is a right angle; definition of right angles OPN and NPL OPN MPL by SSS. %3D and are right triangles Given: ON ML, LP PN and ZOPN ZOPN LPLM M2OPN m/PLM MZOPN m/PLM= 90 by substitution ZPLM is a right angle; definition of right angles OPN MPL by SAS. is a right angle. by Vertical Angles Theorem ; definition of congruent angles 06 ; definition of right angles %3D Given: ON ML, LP PN, and ZOPN ZOPN ZLPM m/OPN m/LPM is a right angle. by Vertical Angles Theorem ; definition of congruent angles 06 = Nd07W by substitution ;definition of right angles ZLPM is a right angle; definition of right angles OPN and NPL and are right triangles OPN MPL by Hypotenuse-Leg Review progress Question 2
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