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Which lines are parallel if mangle4 = mangle5? Justify your answer.
An image with four lines that intersect in pairs is shown.
To determine which lines are parallel if the measure of angle 4 (m∠4) is equal to the measure of angle 5 (m∠5), we need to examine the relationships between the lines.
In the image with four intersecting lines, we can see that there are two pairs of intersecting lines. Let's label the lines as follows:
Line 1: AB
Line 2: CD
Line 3: EF
Line 4: GH
Now, let's focus on angle 4 (m∠4) and angle 5 (m∠5). Since these angles have the same measure, we can conclude that the lines they intersect must be parallel.
Angle 4 (m∠4) is formed by Line 1 (AB) and Line 2 (CD).
Angle 5 (m∠5) is formed by Line 3 (EF) and Line 4 (GH).
Therefore, Line 1 (AB) is parallel to Line 2 (CD), and Line 3 (EF) is parallel to Line 4 (GH) if m∠4 = m∠5.
In summary, if m∠4 = m∠5, Lines 1 and 2 (AB and CD) are parallel, and Lines 3 and 4 (EF and GH) are parallel.