Mathematics, 22.11.2021 14:30 edjiejwi
Given: Point M is the midpoint of LO¯¯¯¯¯¯¯ and NP¯¯¯¯¯¯¯¯ and ∠LNM and ∠OPM are right angles. Prove: ΔLMN≅ΔOPM The students are asked to construct an argument to prove ΔLMN≅ΔOPM. Some of the students' responses are given below. Which of the arguments prove the congruence of the two triangles? Select all that apply. A ∠LNMand ∠OPMare right angles: Given LM¯¯¯¯¯¯¯¯¯is the hypotenuse of ΔLNMand OM¯¯¯¯¯¯¯¯¯is the hypotenuse of ΔOPM: Definition of a hypotenuse Point M is the midpoint of LO¯¯¯¯¯¯¯ and NP¯¯¯¯¯¯¯¯: Given LM¯¯¯¯¯¯¯¯¯≅OM¯¯¯¯¯¯¯¯¯and NM¯¯¯¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯: Definition of midpoint and definition of congruent segments. ΔLNM≅ΔOPM: Hypotenuse-Leg Congruence Theorem B ∠LNMand ∠OPMare right angles: Given ∠LNM≅∠OPM: Right angles are congruent Point M is the midpoint of LO¯¯¯¯¯¯¯ and NP¯¯¯¯¯¯¯¯: Given LM¯¯¯¯¯¯¯¯¯≅OM¯¯¯¯¯¯¯¯¯and NM¯¯¯¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯: Definition of midpoint and definition of congruent ΔLNM≅ΔOPM: SAS Theorem C Point M is the midpoint of LO¯¯¯¯¯¯¯ and NP¯¯¯¯¯¯¯¯: Given LM¯¯¯¯¯¯¯¯¯≅OM¯¯¯¯¯¯¯¯¯and NM¯¯¯¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯: Definition of midpoint and definition of congruent segments. ∠LNM≅∠OPM: Vertical angles are congruent ΔLNM≅ΔOPM: SAS Theorem D Point M is the midpoint of LO¯¯¯¯¯¯¯ and NP¯¯¯¯¯¯¯¯: Given LM¯¯¯¯¯¯¯¯¯≅OM¯¯¯¯¯¯¯¯¯and NM¯¯¯¯¯¯¯¯¯¯≅PM¯¯¯¯¯¯¯¯¯: Definition of midpoint and definition of congruent segments. LN¯¯¯¯¯¯¯¯≅OP¯¯¯¯¯¯¯¯: Congruent Parts of Congruent Triangles are Congruent ΔLNM≅ΔOPM: SSS Theorem E ∠LNMand ∠OPMare right angles: Given ∠LNM≅∠OPM: Right angles are congruent ∠LNM≅∠OPM: Vertical angles are congruent Point M is the midpoint of LO¯¯¯¯¯¯¯ : Given LM¯¯¯¯¯¯¯¯¯≅OM¯¯¯¯¯¯¯¯¯: Definition of midpoint and definition of congruent segments ΔLNM≅ΔOPM: AAS Theorem Group of answer choices
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Given: Point M is the midpoint of LO¯¯¯¯¯¯¯ and NP¯¯¯¯¯¯¯¯ and ∠LNM and ∠OPM are right angles. Prove...
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