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Given: AB ║CD; AF ║EC
Prove: ∠BAF ≅ ∠ECD
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure and we will label further as follows
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| Photo by Math Principles in Everyday Life |
Proof:
1. Statement: AB ║CD; AF ║EC
Reason: Given items
2. Statement: Draw a line from point A to point C.
Reason: Line AC will be used as a transversal line.
3. Statement: ∠FAC ≅ ∠ACE
Reason: If a transversal line AC passes through the parallel lines AF and CE, then their alternating interior angles are congruent.
4. Statement: ∠BAC ≅ ∠ACD
Reason: If a transversal line AC passes through the parallel lines AB and CD, then their alternating interior angles are congruent.
5. Statement: m∠BAF = m∠BAC - m∠FAC
m∠ECD = m∠ACD - m∠ACE
Reason: Subtraction properties of angles
6. Statement: ∠BAF ≅ ∠ECD
Reasons: If ∠BAC ≅ ∠ACD and ∠FAC ≅ ∠ACE, then it follows that ∠BAF ≅ ∠ECD.