Question

Math

Posted 3 months ago

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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.
```

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Answer from Sia

Posted 3 months ago

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.

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