Questions: Consider the given diagram. Identify two ways to prove that 1 m. Include justifications.

Consider the given diagram. Identify two ways to prove that 1 m. Include justifications.
Transcript text: Consider the given diagram. Identify two ways to prove that $1 \backslash \mathrm{~m}$. Include justifications.
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Solution

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Solution Steps

Step 1: Find congruent corresponding angles

Angles 3 and 7 are corresponding angles. Since they have the same measure, they are congruent.

Step 2: Conclude that _l_ and _m_ are parallel

If corresponding angles are congruent, then the lines cut by the transversal are parallel. Therefore, _l_ || _m_.

Step 3: Find congruent alternate interior angles

Angles 4 and 5 are alternate interior angles. They have the same measure and are, therefore, congruent.

Step 4: Conclude that _l_ and _m_ are parallel

If alternate interior angles are congruent, then the lines cut by the transversal are parallel. Therefore, _l_ || _m_.

Final Answer:

Two ways to prove that _l_ || _m_:

  1. ∠3 ≅ ∠7 because they are corresponding angles and have the same measure. Since corresponding angles are congruent, _l_ || _m_.

  2. ∠4 ≅ ∠5 because they are alternate interior angles and have the same measure. Since alternate interior angles are congruent, _l_ || _m_.

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