How do you prove two lines are parallel that are cut by a transversal?
If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.
How do you prove two lines are parallel?
To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.
Do the two lines have to be parallel to be cut by a transversal?
If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent. If interior angles on the same side of the transversal sum to 180, then lines are parallel.
What are five ways to prove two lines are parallel?
Ways to Prove Two Lines Parallel
- Show that corresponding angles are equal.
- Show that alternative interior angles are equal.
- Show that consecutive interior angles are supplementary.
- Show that consecutive exterior angles are supplementary.
- In a plane, show that the lines are perpendicular to the same line.
When two parallel lines are cut by a transversal how many pairs of corresponding angles are formed?
four pairs
When a transversal intersects with two parallel lines eight angles are produced. The eight angles will together form four pairs of corresponding angles.
What happens when 2 lines are parallel?
Note that two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.
What theorem is if two parallel lines are cut by a transversal then corresponding angles are congruent?
alternate exterior angles
AEA Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
Which theorem states that if two parallel lines cut by a transversal interior angles on the same side are supplementary?
alternate interior angles
Theorem 10.5: If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary angles….Geometry.
| Statements | Reasons | |
|---|---|---|
| 3. | ?1 and?3 are alternate interior angles | Definition of alternate interior angles |
What is parallel lines cut by a transversal?
Two lines cut by a transversal line are parallel when the alternate interior angles are equal. Alternate interior angles are a pair of angles found in the inner side but are lying opposite each other.
Which of the following proves that two lines are parallel when the lines are cut by a transversal select all that apply?
If two lines are cut by a transversal and the alternate exterior angles are equal, then the two lines are parallel. Angles can be equal or congruent; you can replace the word “equal” in both theorems with “congruent” without affecting the theorem. So if ∠B and ∠L are equal (or congruent), the lines are parallel.
When two parallel lines are cut by a transversal interior angles are supplementary?
If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel.
What is line that cuts across two or more parallel lines?
Definition: A line that cuts across two or more (usually parallel) lines. In the figure below, the line AB is a transversal. It cuts across the parallel lines PQ and RS. If it crosses the parallel lines at right angles it is called a perpendicular transversal.
How are perpendicular lines different to intersecting lines?
Perpendicular lines and intersecting lines are the same because they both describe 2 lines that cross one another… They are different because perpendicular lines cross one another in a specific way. The intersection of perpendicular lines forms 90 degree angles, while intersecting lines just describes 2 lines crossing.
What is the angle between parallel lines?
Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles. Angles that are on the opposite sides of the transversal are called alternate angles e.g. 1 + 8.
Are parallel lines congruent?
If two parallel lines are cut by a straight line (transversal), then the corresponding angles around each intersection are equal in measure or we can say mathematically as these angles are congruent. If two parallel lines are cut by a straight line (transversal) then the alternate interior angles are congruent.
