The missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:
a. Corresponding angles
b. Vertical Angles, and
c. Alternate interior angles
- Two angles lying opposite each other along a transversal, and are within the two lines crossed by the transversal are referred to as alternate interior angles.
- According to the Alternate Interior Angles Theorem, the two alternate interior angles are congruent to each other.
- <em>Let's state out our </em><em>proof </em><em>using the image given:</em>
<em />
<em><u>Statement 1</u></em>: line l is parallel to line m
Reason: Given
<em><u>Statement 2:</u></em>
Reason: Corresponding Angles <em>(both angles occupy the same corner, hence they correspond to each other. </em><em>Corresponding angles</em><em> have the same measure).</em>
<u><em>Statement 3: </em></u>
Reason: Vertical angles<em> (both angles are directly opposite each other as they share the same point, which makes them </em><em>vertical angles</em><em>. </em><em>Vertical angles</em><em> have equal measure).</em>
<em><u>Statement 4: </u></em><em><u /></em>
Reason: Alternate Interior Angles <em>(applying the </em><em>transitive property</em><em> which says if a = b, and b = c, then a = c, therefore, since </em><em>)</em>
In conclusion, the missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:
a. Corresponding angles
b. Vertical Angles, and
c. Alternate interior angles
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