A. Triangle Inequality Theorem 3 (S1 + S2 > S3) Given: Δ ΑSE Prove: SA + AE > SE Extend SA to F so that AF = AE E Statement Reason 1. 1. By construction (Extend SA to F such that AF = AE) 2. A AFE is an isosceles 2. 3. 3. Isosceles Triangle Theorem (equal sides contain equal angles) 4. The whole angle is greater than the part 4. MLFES > mz1 5. MLFES > mL2 5. Substitution Property, using the step 3 (since mz1 = m22) » Ss) 6. Triangle Inequality Theorem 2 (Aa (Greater angle has greater opposite side) 7. Substitution Property, replace SF by SA + AF (since SF = SA + AF) 6. 7. SA + AF > Se 8. SA + AE > SE 8.

A. Triangle Inequality Theorem 3 (S1 + S2 > S3) Given: Δ ΑSE Prove: SA + AE > SE Extend SA to F so that AF = AE E Statement Reason 1. 1. By construction (Extend SA to F such that AF = AE) 2. A AFE is an isosceles 2. 3. 3. Isosceles Triangle Theorem (equal sides contain equal angles) 4. The whole angle is greater than the part 4. MLFES > mz1 5. MLFES > mL2 5. Substitution Property, using the step 3 (since mz1 = m22) » Ss) 6. Triangle Inequality Theorem 2 (Aa (Greater angle has greater opposite side) 7. Substitution Property, replace SF by SA + AF (since SF = SA + AF) 6. 7. SA + AF > Se 8. SA + AE > SE 8.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 30E

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