Question
Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answers.
Which lines are parallel if mangle4 = mangle5? Justify your answer.
An image with four lines that intersect in pairs is shown.
Without the image provided, it is not possible to determine which lines are parallel if m∠4 = m∠5. Please provide the image for further analysis.
To determine which lines are parallel when m∠4 = m∠5, we first need to understand the concept of alternate interior angles.
Alternate interior angles are a pair of angles that lie on opposite sides of the transversal line, and they are congruent (have equal measures) when the lines intersect by a transversal. In other words, if two lines are crossed by another line (transversal), and the alternate interior angles formed by the transversal are congruent, then the two lines are parallel.
Here's how you can use this information to find the parallel lines in your image:
1. Identify the pair of angles, m∠4 and m∠5, that are given to be congruent.
2. Locate the transversal line that intersects the other lines in the image. This transversal line will form alternate interior angles with the given angles.
3. Look for another pair of angles that are congruent to each other and lie on the same side of the transversal as m∠4 and m∠5. These angles are also alternate interior angles.
4. The lines corresponding to these congruent pairs of alternate interior angles are the parallel lines.
To justify your answer, you can provide a clear explanation of the congruent pairs of alternate interior angles in the image and how they relate to the parallel lines.
To determine which lines are parallel when m∠4 = m∠5, we need to examine the angles formed by the intersecting lines.
If m∠4 = m∠5, it means that the two angles are congruent, or have the same measure. According to the Transversal Line Theorem, if a transversal intersects two lines and creates congruent corresponding angles, then the lines are parallel.
Therefore, the lines that are parallel when m∠4 = m∠5 are the lines that have corresponding congruent angles.