Alternate exterior angles are congruent if the lines crossed by the transversal are parallel. If alternate exterior angles are congruent, then the lines are parallel. At each intersection, the corresponding angles lie at the same place.
How do you prove that alternate exterior angles are congruent?
Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. The proof of this theorem is very similar to that of the Alternate Interior Angles Theorem.
Are alternate side exterior angles congruent?
The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent .
Are alternate exterior angles congruent or supplementary?
Since alternate interior and alternate exterior angles are congruent and since linear pairs of angles are supplementary, same side angles are supplementary.
Is alternate exterior angles equal?
Thus, the two exterior angles which form at the alternate ends of the transversals in the exterior part are considered as the pair of alternate exterior angles and they are always equal. We get two such pairs of alternate exterior angles when a transversal cuts two parallel lines.
Do alternate exterior angles add up to 180?
If the transversal cuts across parallel lines (the usual case) then exterior angles are supplementary (add to 180°). So in the figure above, as you move points A or B, the two angles shown always add to 180°.
How do you do alternate exterior angles theorem?
https://www.youtube.com/embed/W-V51Hoc0Nw
Are all exterior angles congruent?
All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent. The picture above shows two parallel lines with a transversal.
What does alternate exterior mean in math?
Alternate exterior angles are formed by a transversal intersecting two parallel lines . They are located outside the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate exterior angles.
Can alternate exterior angles not be congruent?
Alternate exterior angles are always congruent.
Are alternate exterior angles congruent when lines are parallel?
If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel.
Are exterior angles supplementary?
The theorem states that same-side exterior angles are supplementary, meaning that they have a sum of 180 degrees.
Are alternate interior angles congruent?
There’s only one other pair of alternate interior angles and that’s angle 3 and its opposite side in between the parallel lines which is 5. So alternate interior angles will always be congruent and always be on opposite sides of this transversal.
Are same side angles congruent?
Same side interior angles are congruent when lines are parallel.
Why exterior angles add up to 360?
The sum of the exterior angles of any polygon (remember only convex polygons are being discussed here) is 360 degrees. … Because the exterior angles are supplementary to the interior angles, they measure, 130, 110, and 120 degrees, respectively. Summed, the exterior angles equal 360 degreEs.
Are alternate exterior angles complementary?
Yes alternate exterior angles are supplementary.
What angles are alternate exterior angles?
Alternate exterior angles are the pair of angles that lie on the outer side of the two parallel lines but on either side of the transversal line.
How are the alternate interior angles theorem and the alternate exterior angles theorem different?
If lines are parallel then corresponding angles are congruent, alternate interior angles are congruent and alternate exterior angles are congruent. If lines are parallel, then same side interior angles are supplementary and same side exterior angles are supplementary.
Why are alternate interior angles always congruent?
The alternate interior angles theorem states that, the alternate interior angles are congruent when the transversal intersects two parallel lines. Hence, it is proved. Alternate interior angles can be calculated by using properties of the parallel lines. Two consecutive interior angles are (2x + 10) ° and (x + 5) °.