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Proof of the Pythagorean Theorem Given: Triangle ABC is a right Triangle, and CD is an altitude Prove: a + b² = c? a b Statement Reason 1.Triangle ABC is a right Triangle, and 1. CD is an altitude 2. MLBDC = 90 2. MLADC = 90

Proof of the Pythagorean Theorem Given: Triangle ABC is a right Triangle, and CD is an altitude Prove: a + b² = c? a b Statement Reason 1.Triangle ABC is a right Triangle, and 1. CD is an altitude 2. MLBDC = 90 2. MLADC = 90

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.
Chapter1: Line And Angle Relationships
Section1.4: Relationships: Perpendicular Lines
Problem 30E
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Given the proof below, what is the reason for #12 Proof of the Pythagorean Theorem Given: Triangle ABC is a right Triangle, and CD is an altitude Prove: a + b2 = c² a b Statement Reason 1.Triangle ABC is a right Triangle, and 1. CD is an altitude 2. MLBDC = 90 2. MLADC = 90 3. m <A = m<A 3. 4. т < В %3D т< В 4. 5. т < ACB — т<CDB — т< ADC 5. 6. ΔACB~ΔCDB ~ΔADC 6. b_f 7. 7. %3D S. b? = cf , a? = ce S. Cross multiplication 9. a? + b? = cf + a² 9. 10. a? + b? = cf + ce 10. 11. a? + b² = c(f + e) 11. 12. a+b =c-c 12. 13. 13.a?
Transcribed Image Text:Given the proof below, what is the reason for #12 Proof of the Pythagorean Theorem Given: Triangle ABC is a right Triangle, and CD is an altitude Prove: a + b2 = c² a b Statement Reason 1.Triangle ABC is a right Triangle, and 1. CD is an altitude 2. MLBDC = 90 2. MLADC = 90 3. m <A = m<A 3. 4. т < В %3D т< В 4. 5. т < ACB — т<CDB — т< ADC 5. 6. ΔACB~ΔCDB ~ΔADC 6. b_f 7. 7. %3D S. b? = cf , a? = ce S. Cross multiplication 9. a? + b? = cf + a² 9. 10. a? + b? = cf + ce 10. 11. a? + b² = c(f + e) 11. 12. a+b =c-c 12. 13. 13.a?
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