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I. Given: ALMN; mLL >mLN M Prove: MN > LM Proof: Indirect Proof: Assume MN LM Statements Reasons 1. By assumption MN 1. MN = LM or LM 2.Definition of MN 2. Considering LM : If MN LM then 3. Base angles of isosceles As are congruent 3. L 4. The conclusion that 4. The assumption MN IMis 7. the given that 5. Theorem 5. Considering MN < LM If MN LM Then m 7. < m 7. 6. The conclusion that m 6. The assumption is 7. m 7. Therefore, must be 7.

I. Given: ALMN; mLL >mLN M Prove: MN > LM Proof: Indirect Proof: Assume MN LM Statements Reasons 1. By assumption MN 1. MN = LM or LM 2.Definition of MN 2. Considering LM : If MN LM then 3. Base angles of isosceles As are congruent 3. L 4. The conclusion that 4. The assumption MN IMis 7. the given that 5. Theorem 5. Considering MN < LM If MN LM Then m 7. < m 7. 6. The conclusion that m 6. The assumption is 7. m 7. Therefore, must be 7.

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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Direction: Prove that one side is greater than the other side by completing the two-column proof below. HTAM L. Given: ALMN; mLL >m2N M Prove: MN > LM Proof: Indirect Proof: Assume MN LM Statements Reasons 1. By assumption MN 1. =LM or MN LM く %3D 2.Definition of MN 2. Considering LM If MN LM welgns 3. Base angles of isosceles As are congruent then 3. 2 4. The conclusion that >め 4. The assumption MN TMİ. the given that Theorem 5. Considering MN LM MN If LM Then m <m² 6. The conclusion that m 6. The assumption is <m The given that m L>m N 7.The assumption that contradicts the known fact that m 7. Therefore, must be 5.
Transcribed Image Text:Direction: Prove that one side is greater than the other side by completing the two-column proof below. HTAM L. Given: ALMN; mLL >m2N M Prove: MN > LM Proof: Indirect Proof: Assume MN LM Statements Reasons 1. By assumption MN 1. =LM or MN LM く %3D 2.Definition of MN 2. Considering LM If MN LM welgns 3. Base angles of isosceles As are congruent then 3. 2 4. The conclusion that >め 4. The assumption MN TMİ. the given that Theorem 5. Considering MN LM MN If LM Then m <m² 6. The conclusion that m 6. The assumption is <m The given that m L>m N 7.The assumption that contradicts the known fact that m 7. Therefore, must be 5.
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