Mark constructed $\overleftrightarrow{C E}$ parallel to $\overleftrightarrow{A B}$ through point $C$

Which of the following statements best justifies why $\overleftrightarrow{C E}$ is parallel to $\overleftrightarrow{A B} ?$

Choose 1 answer:
(A) Lines perpendicular to the same transversal are parallel.
(B) Lines with congruent same-side interior angles are parallel.
(C) Lines with congruent alternate interior angles are parallel.
(D) Lines with congruent corresponding angles are parallel.

Question

Mark constructed $\overleftrightarrow{C E}$ parallel to $\overleftrightarrow{A B}$ through point $C$

Which of the following statements best justifies why $\overleftrightarrow{C E}$ is parallel to $\overleftrightarrow{A B} ?$

Choose 1 answer:
(A) Lines perpendicular to the same transversal are parallel.
(B) Lines with congruent same-side interior angles are parallel.
(C) Lines with congruent alternate interior angles are parallel.
(D) Lines with congruent corresponding angles are parallel.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Given that line $ \overleftrightarrow{CE} $ is constructed parallel to line $ \overleftrightarrow{AB} $ through point $C$, we need to identify the statement that justifies this parallelism. ‖ ‖ step 2 ⋮ From the given information and the diagram, we can infer that the lines are parallel by definition, as it is stated that line $ \overleftrightarrow{CE} $ is constructed to be parallel to line $ \overleftrightarrow{AB} $. ‖ ‖ step 3 ⋮ However, to choose the best answer from the given options, we need to consider the properties of parallel lines and the corresponding angles they form with a transversal. ‖ ‖ step 4 ⋮ If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. This is a property of parallel lines. ‖ ‖ step 5 ⋮ Since line $ \overleftrightarrow{AD} $ acts as a transversal for lines $ \overleftrightarrow{CE} $ and $ \overleftrightarrow{AB} $, and the corresponding angles formed would be congruent by the construction of parallel lines, the correct justification is that lines with congruent corresponding angles are parallel. ‖ ∻Answer∻ ⚹ (D) Lines with congruent corresponding angles are parallel. ⚹ ∻Key Concept∻ ⚹Corresponding Angles Postulate⚹ ∻Explanation∻ ⚹When two lines are cut by a transversal, if the corresponding angles are congruent, the lines are parallel. This is known as the Corresponding Angles Postulate.⚹◊What is the relationship between alternate interior angles and parallel lines in geometry?⍭ Generate me a similar question◊

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