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
Related questions
Question
Supply the missing statements and reasons in the proof.
![F
A. Triangle Inequality Theorem 3 (S1 + S2 > S3)
Given: ΔΑSE
Prove: SA + AE > SE
A
A
Extend SA to F so that AF = AE
E
S
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. MZFES > mz1
5. Substitution Property, using the step 3 (since mz1 = m2)
6. Triangle Inequality Theorem 2 (Aa → Ss)
(Greater angle has greater opposite side)
7. Substitution Property, replace SF by SA + AF (since SF = SA + AF)
5. MLFES > m2
6.
7. SA + AF > Se
8. SA + AE > SE
8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F973071af-2c20-464a-8506-110f32900355%2F564e7ad5-9c45-4e9f-b1b1-f6fa9443f697%2F8s1bwhk_processed.png&w=3840&q=75)
Transcribed Image Text:F
A. Triangle Inequality Theorem 3 (S1 + S2 > S3)
Given: ΔΑSE
Prove: SA + AE > SE
A
A
Extend SA to F so that AF = AE
E
S
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. MZFES > mz1
5. Substitution Property, using the step 3 (since mz1 = m2)
6. Triangle Inequality Theorem 2 (Aa → Ss)
(Greater angle has greater opposite side)
7. Substitution Property, replace SF by SA + AF (since SF = SA + AF)
5. MLFES > m2
6.
7. SA + AF > Se
8. SA + AE > SE
8.
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