What is an example of alternate interior angles Theorem?
The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent . So, in the figure below, if k∥l , then ∠2≅∠8 and ∠3≅∠5 . Proof.
What are alternate angles on parallel lines?
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Each pair of alternate angles around the transversal are equal to each other. The two angles can either be alternate interior angles or alternate exterior angles.
What is the alternate exterior angle of ∠ 7?
The term alternate exterior angles is often used when two lines are cut by a third line, a transversal . The Alternate Exterior Angles Theorem states that if k and l are parallel , then the pairs of alternate exterior angles are congruent . That is, ∠1≅∠7 and ∠4≅∠6 .
How do you prove the alternate angle theorem?
Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent. To prove: If two parallel lines are cut by a transversal, then the alternate interior angles are equal.
What is the alternate interior angle theorem converse?
By alternate interior angle theorem converse, if a transversal intersects two lines such that a pair of interior angles are equal, then the two lines are parallel. Refer to the figure above. We have: If two lines are parallel, then the pair alternate exterior angles formed are congruent.
How to prove that two lines are parallel to each other?
If the alternate interior angles produced by the transversal line on two coplanar are congruent, then the two lines are parallel to each other. ∠2 = ∠5, which are corresponding angles. Therefore, a is parallel to b. Co-interior angles or Consecutive interior angles are the two angles that are on the same side of the transversal.
What are the pair of angles of in parallel lines?
The pair of angles of in parallel lines are corresponding, alternate interior, alternate exterior and interior angles of the same side of the transversal. Q.3. What are the properties of parallel lines?