A geometry teacher provides her class with this problem N O M Given Point M is the midpoint of LO and NP and ZLNM and ZOPM are right angles Prove ALMN AOPM The students are asked to construct an argument to prove ALMN AOPM Some of the students' responses are given below Which of the arguments prove the congruence of the two triangles Select all that apply LLNM and ZOPM are right angles Given LM is the hypotenuse of ALNM and OM is the hypotenuse of AOPM Definition of a hypotenuse A Point M is the midpoint of LO and NP Given LM OM and NM PM Definition of midpoint and definition of congruent segments ALNM AOPM Hypotenuse Leg Congruence Theorem ZLNM and ZOPM are right angles Given LLNM ZOPM Right angles are congruent B Point M is the midpoint of LO and NP Given LM OM and NM PM Definition of midpoint and definition of congruent ALNM AOPM SAS Theorem Point M is the midpoint of LO and NP Given LM OM and NM PM Definition of midpoint and definition of congruent C segments ZLNM ZOPM Vertical angles are congruent ALNM AOPM SAS Theorem Point M is the midpoint of LO and NP Given LM OM and NM PM Definition of midpoint and definition of congruent D segments LN OP Congruent Parts of Congruent Triangles are Congruent ALNM AOPM SSS Theorem ZLNM and ZOPM are right angles Given LLNM ZOPM Right angles are congruent ZLNM ZOPM Vertical angles are congruent E Point M is the midpoint of LO Given LM OM Definition of midpoint and definition of congruent segments ALNM AOPM AAS Theorem

Question

A geometry teacher provides her class with this problem  N O M Given  Point M is the midpoint of LO and NP and ZLNM and ZOPM are right angles  Prove  ALMN   AOPM The students are asked to construct an argument to prove ALMN   AOPM  Some of the students' responses are given below  Which of the arguments prove the congruence of the two triangles  Select all that apply    LLNM and ZOPM are right angles  Given   LM is the hypotenuse of ALNM and OM is the hypotenuse of AOPM  Definition of a hypotenuse A   Point M is the midpoint of LO and NP  Given   LM   OM and NM   PM  Definition of midpoint and definition of congruent segments    ALNM   AOPM  Hypotenuse Leg Congruence Theorem  ZLNM and ZOPM are right angles  Given   LLNM   ZOPM  Right angles are congruent B   Point M is the midpoint of LO and NP  Given   LM   OM and NM   PM  Definition of midpoint and definition of congruent   ALNM   AOPM  SAS Theorem   Point M is the midpoint of LO and NP  Given   LM   OM and NM   PM  Definition of midpoint and definition of congruent C segments    ZLNM   ZOPM  Vertical angles are congruent   ALNM   AOPM  SAS Theorem   Point M is the midpoint of LO and NP  Given   LM   OM and NM   PM  Definition of midpoint and definition of congruent D segments    LN   OP  Congruent Parts of Congruent Triangles are Congruent   ALNM   AOPM  SSS Theorem   ZLNM and ZOPM are right angles  Given   LLNM   ZOPM  Right angles are congruent   ZLNM   ZOPM  Vertical angles are congruent E   Point M is the midpoint of LO   Given   LM   OM   Definition of midpoint and definition of congruent segments   ALNM   AOPM  AAS Theorem

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A geometry teacher provides her class with this problem. N O M Given: Point M is the midpoint of LO and NP and ZLNM and

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