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Reasons a. b. c. Vertical Angles- d.

Reasons a. b. c. Vertical Angles- d.

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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M Given: PM bisects ZLPN P 1 Prove: 2 41 Statements Reasons a. PM bisects LPN b. 22 23 a. b. c. Vertical Angles Are a с. d. 22 21 d. GEOMETRY Name Notes Section 2.6 Day 2 Proofs With Definitions Today we will be looking at proofs which require definitions. Remember, definitions are always biconditional – they are true both ways! Definition of a Right Angle IF and angle's measure is 90° THEN it is a right angle OR IF an angle is a right angle THEN its measure is 90° Definition of Complementary Angles Definition of Supplementary Angles IF two angles sum to 90 THEN they are complementary IF two angles sum to 180° THEN they are supplementary OR OR IF two angles are supplementary IF two angles are complementary THEN they sum to 90° THEN they sum to 180° 1. Given: ZABE is a right angle. Prove: 24 is complementary to 42 2. Given: 2 is supplementary to 23 Prove: 45 is supplementary to 43 D A B 2 3 4 E Statements Reasons Statements Reasons 1. ZABE is a right angle 2. MLABE = 90° 1. 1. 1. 2. 2. 2. 3. Angle Addition Postulate 3. 3. 3. 4. 4. 4. 4. 5. Vertical Angles Theorem 5. 5. 5. 6. 6. 6. 6. 7. Substitution Property of Equality 8. 7. 8. 4 is complementary to 2
Transcribed Image Text:M Given: PM bisects ZLPN P 1 Prove: 2 41 Statements Reasons a. PM bisects LPN b. 22 23 a. b. c. Vertical Angles Are a с. d. 22 21 d. GEOMETRY Name Notes Section 2.6 Day 2 Proofs With Definitions Today we will be looking at proofs which require definitions. Remember, definitions are always biconditional – they are true both ways! Definition of a Right Angle IF and angle's measure is 90° THEN it is a right angle OR IF an angle is a right angle THEN its measure is 90° Definition of Complementary Angles Definition of Supplementary Angles IF two angles sum to 90 THEN they are complementary IF two angles sum to 180° THEN they are supplementary OR OR IF two angles are supplementary IF two angles are complementary THEN they sum to 90° THEN they sum to 180° 1. Given: ZABE is a right angle. Prove: 24 is complementary to 42 2. Given: 2 is supplementary to 23 Prove: 45 is supplementary to 43 D A B 2 3 4 E Statements Reasons Statements Reasons 1. ZABE is a right angle 2. MLABE = 90° 1. 1. 1. 2. 2. 2. 3. Angle Addition Postulate 3. 3. 3. 4. 4. 4. 4. 5. Vertical Angles Theorem 5. 5. 5. 6. 6. 6. 6. 7. Substitution Property of Equality 8. 7. 8. 4 is complementary to 2
2.6 Day 1 Homework: I can prove statements about segments and angles. Given: ZLMO S ENMP Prove: LMPS ZNMO Statements Reasons a. b. MZLMO = MZNMP b. c. MZLMO=mzLMP+m<PMO C. MZNMP=mZ NMO +mzPMO d. mzLMP+MLPMO=m2 NMO +M<PMO e. mzLMP=mzNMO f. ZLMP S ZNMO f. Given: AC BD Prove: AB CD Statements Reasons a. AC BD b. AC = BD a. b. c. AB + BC = AC C. d. BC + = d. Segment Addition Postulate e. AB + BC = BC + CD e f. Subtraction Property g. Definition of Congruent Segments f. g. Given: B is the midpoint of AC B Prove: AB = AC Statements Reasons a. Bis the midpoint of AC a. b. AB = BC b. с. АВ + ВС AC с. d. AB + AB = AC d. e. 2AB = AC e. f. AB = AC f.
Transcribed Image Text:2.6 Day 1 Homework: I can prove statements about segments and angles. Given: ZLMO S ENMP Prove: LMPS ZNMO Statements Reasons a. b. MZLMO = MZNMP b. c. MZLMO=mzLMP+m<PMO C. MZNMP=mZ NMO +mzPMO d. mzLMP+MLPMO=m2 NMO +M<PMO e. mzLMP=mzNMO f. ZLMP S ZNMO f. Given: AC BD Prove: AB CD Statements Reasons a. AC BD b. AC = BD a. b. c. AB + BC = AC C. d. BC + = d. Segment Addition Postulate e. AB + BC = BC + CD e f. Subtraction Property g. Definition of Congruent Segments f. g. Given: B is the midpoint of AC B Prove: AB = AC Statements Reasons a. Bis the midpoint of AC a. b. AB = BC b. с. АВ + ВС AC с. d. AB + AB = AC d. e. 2AB = AC e. f. AB = AC f.
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