Geometry - Parallel Lines

1) What is the relationship of slopes between parallel lines?

Opposite

Opposite reciprocals

Reciprocal

Equal

The relationship of slopes between parallel lines is that they are equal. This means that if two lines are parallel, their slopes will have the same value.

Explanation

The relationship of slopes between parallel lines is that they are equal. This means that if two lines are parallel, their slopes will have the same value.

2) Which of the following is always congruent even if lines are not parallel?

Consecutive interior angles

Vertical angles

Alternate exterior angles

Corresponding angles

Vertical angles are always congruent, regardless of whether the lines are parallel or not. Vertical angles are formed by two intersecting lines and are opposite to each other. They have equal measures and are congruent because they are formed by the same pair of intersecting lines. This property holds true for any pair of vertical angles, regardless of the orientation of the lines.

Explanation

Vertical angles are always congruent, regardless of whether the lines are parallel or not. Vertical angles are formed by two intersecting lines and are opposite to each other. They have equal measures and are congruent because they are formed by the same pair of intersecting lines. This property holds true for any pair of vertical angles, regardless of the orientation of the lines.

3) Which of the following are methods to prove two lines are parallel when cut by a transversal?

Alternate exterior angles are congruent.

Consecutive interior angles are congruent.

Corresponding angles are supplementary.

Alternate interior angles are congruent.

The method to prove two lines are parallel when cut by a transversal is by showing that the alternate interior angles are congruent. This means that the angles on the inside of the two lines, but on opposite sides of the transversal, are equal in measure. If the alternate interior angles are congruent, it indicates that the lines are parallel.

Explanation

The method to prove two lines are parallel when cut by a transversal is by showing that the alternate interior angles are congruent. This means that the angles on the inside of the two lines, but on opposite sides of the transversal, are equal in measure. If the alternate interior angles are congruent, it indicates that the lines are parallel.

4) What is the relationship of the slopes on perpendicular lines?

Opposite

Opposite reciprocals

Reciprocals

Equal

Perpendicular lines have slopes that are opposite reciprocals of each other. This means that if one line has a slope of m, the perpendicular line will have a slope of -1/m.

Explanation

Perpendicular lines have slopes that are opposite reciprocals of each other. This means that if one line has a slope of m, the perpendicular line will have a slope of -1/m.

5) Which of the following angle pairs are congruent because parallel lines are cut by a transversal?

Corresponding

Alternate interior

Alternate exterior

When parallel lines are cut by a transversal, corresponding angles, alternate interior angles, and alternate exterior angles are congruent. Corresponding angles are formed when a transversal intersects two parallel lines and are located in the same relative position on each line. Alternate interior angles are located on opposite sides of the transversal and inside the two parallel lines. Alternate exterior angles are located on opposite sides of the transversal and outside the two parallel lines. Therefore, all three angle pairs mentioned in the answer (corresponding, alternate interior, and alternate exterior) are congruent when parallel lines are cut by a transversal.

Explanation

When parallel lines are cut by a transversal, corresponding angles, alternate interior angles, and alternate exterior angles are congruent. Corresponding angles are formed when a transversal intersects two parallel lines and are located in the same relative position on each line. Alternate interior angles are located on opposite sides of the transversal and inside the two parallel lines. Alternate exterior angles are located on opposite sides of the transversal and outside the two parallel lines. Therefore, all three angle pairs mentioned in the answer (corresponding, alternate interior, and alternate exterior) are congruent when parallel lines are cut by a transversal.

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