What is alternate interior angles theorem in math?

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 .

What is meant by co-interior angles?

Co-interior angles lie between two lines and on the same side of a transversal. In each diagram the two marked angles are called co-interior angles. If the two lines are parallel, then co-interior angles add to give 180o and so are supplementary.

How do you solve the alternate interior angles theorem?

Since a straight angle measures 180 degrees, angle x + 58 = 180 and 180 – 58 = angle x, so angle x = 122. Finally, angle x and angle z are alternate interior angles, and we know that alternate interior angles are equal. So, angle x = 122 then angle z = 122. 2.

How do you prove the alternate interior angles theorem?

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) °.

What is the difference between alternate interior angles and alternate angles?

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.

What does alternate mean in maths?

The word ‘alternate’ is usually used with pairs of angles, to indicate that each is on opposite sides of a line. In the figure below, the two angles are called alternate angles because they are on opposite sides of the sloping transversal line.

What is alternate and corresponding angle?

One of corresponding angles is always interior (in between parallel lines) and another – exterior (outside of the area in between parallel lines). Two acute angles a and c’ , formed by different parallel lines when intersected by a transversal, lying on the opposite sides from a transversal, are called alternate.

What are alternate and corresponding angles?

Which angles are alternate interior angles?

Alternate Interior angles are congruent.

What are alternate interior and exterior angles?

– The alternate interior angles are equal in measure. – They lie on the alternate sides of the transversal. – They lie in between the interior of the two lines. – In other words, the angles that lie on the inner side of the parallel lines but on the opposite sides of the transversal.

Which angles are consecutive interior angles?

Consecutive interior angles have different vertices.

What are alternate exterior angles in math terms?

When the two lines are parallel,the alternate exterior angles are congruent (they have the same measure).