Are alternate exterior angles congruent or supplementary?

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.

Are alternate interior and 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.

Why are the alternate exterior angles congruent?

Alternate exterior angles are congruent if the lines crossed by the transversal are parallel. At each intersection, the corresponding angles lie at the same place. The alternate exterior angles that lie outside the lines are intercepted by the transversal. These angles are supplementary to the adjacent angles.

Are alternate congruent angles congruent?

Alternate Interior Angle Theorem The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .

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.

What are the properties of alternate exterior angles?

The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent . ∠1≅∠7 and ∠4≅∠6 .

Are linear pair angles always congruent?

Linear pairs are congruent. Adjacent angles share a vertex. Adjacent angles overlap. Supplementary angles form linear pairs.

Do alternate exterior angles add 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°.

Which angles are congruent?

Congruent angles are angles with exactly the same measure. Example: In the figure shown, ∠A is congruent to ∠B ; they both measure 45° . Congruence of angles in shown in figures by marking the angles with the same number of small arcs near the vertex (here we have marked them with one red arc).

How are alternate exterior angles formed?

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.

When is an alternate exterior angle congruent with an interior angle?

Alternate exterior angles are congruent if the lines intercepted by the transversal are parallel. The lines are parallel if alternate interior, alternate exterior, or corresponding angles are congruent.

When do you use an alternate exterior angle?

Alternate exterior angle states that, the resulting alternate exterior angles are congruent when two parallel lines are cut by a transversal. Consider the diagram above. The two lines are parallel.

Is the converse of the alternate exterior angles theorem true?

The converse of this theorem is also true; that is, if two lines k and l are cut by a transversal so that the alternate exterior angles are congruent, then k ∥ l .

How are the angles of the lines congruent?

If alternate exterior angles are congruent, then the lines are parallel. At each intersection, the corresponding angles lie at the same place. The alternate exterior angles that lie outside the lines are intercepted by the transversal. These angles are supplementary to the adjacent angles.