Given: BC || DE, and ∠GAC ≅ ∠AFD. Prove: Statement Reason 1. ∠GAC ≅ ∠AFD given 2. ∠GAC ≅ ∠AFE For parallel lines cut by a transv
ersal, corresponding angles are congruent. 3. 4. ∠AFD and ∠AFE are supplementary. Linear Pair Theorem 5. m∠AFD = m∠AFE = 90° If two congruent angles are supplementary, then each angle is a right angle. 6. definition of perpendicular lines What is the missing step in the proof? A. Statement: ∠GAC and ∠GAB are supplementary. Reason: Linear Pair Theorem B. Statement: ∠AFE ≅ ∠AFD Reason: Transitive Property of Equality C. Statement: ∠GAC ≅ ∠BAF Reason: Vertical Angles Theorem D. Statement: ∠GAC and ∠AFD are supplementary. Reason: Linear Pair Theorem Reset
2 answers:
Answer:
The correct Option is B. Statement: ∠AFE ≅ ∠AFD Reason: Transitive Property of Equality
Step-by-step explanation:
A is true, but unnecessary. Because after proving statement A, it will imply BC ⊥ GH but that is not required.
C is also true, but this condition is also not useful in the proving the required statement which is to be proved.
D can be proved. But that is not required hence this will make the solution much bigger.
Now, let us take B. we need 2 facts to prove that lines are perpendicular when parallel lines with a transversal is given.
1. We need that the line we want to show perpendicular to the transversal and the transversal itself to form supplementary angles.
2. And the supplementary angles thus formed to be equal.
Condition 1 has been proved by the step 4.
So it must be condition 2 that you need in step 3.
∠AFD = ∠AFE
Reason : Two angles that are equal to the same angle must themselves be equal.( Transitive property of equality)
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