When two parallel lines are cut by a transversal how many pairs of alternate interior angles are formed Brainly?

The term alternate interior angles is often used when two lines are cut by a third line, a transversal .

In the figure above, line t is a transversal cutting lines k and l , and there are two pairs of alternate interior angles:

∠ 2 and ∠ 8

∠ 3 and ∠ 5

The Alternate Interior Angles Theorem states that if k and l are parallel , then the pairs of alternate interior angles are congruent . That is,

∠ 2 ≅ ∠ 8 and ∠ 3 ≅ ∠ 5 .

The converse of this theorem is also true.

Alternate interior angles are formed by a transversal intersecting two parallel lines . They are located between the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate interior angles. Alternate interior angles are congruent, meaning they have equal measure.

parallel lines angles congruence interior transversal

When we have two parallel lines that are intersected by a transversal, and again my parallel lines are identified by using the same number of arrows, then two special angles are congruent and that is alternate interior angles. So let's examine these two words, alternate means on opposite sides, interior means within or in between. So here we have our two parallel lines, our alternate interior angles are going to be the angles that are inside and on opposite sides of the transversal. So angle 4 is inside and its opposite side would be 6 so those two angles will be 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.

Two lines that are stretched into infinity and still never intersect are called coplanar lines and are said to be parallel lines. The symbol for "parallel to" is //.

If we have two lines (they don't have to be parallel) and have a third line that crosses them as in the figure below - the crossing line is called a transversal:

In the following figure:

If we draw to parallel lines and then draw a line transversal through them we will get eight different angles.

The eight angles will together form four pairs of corresponding angles. Angles F and B in the figure above constitutes one of the pairs. Corresponding angles are congruent if the two lines are parallel. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs.

Angles that are in the area between the parallel lines like angle H and C above are called interior angles whereas the angles that are on the outside of the two parallel lines like D and G are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles e.g. H and B.

Angles that share the same vertex and have a common ray, like angles G and F or C and B in the figure above are called adjacent angles. As in this case where the adjacent angles are formed by two lines intersecting we will get two pairs of adjacent angles (G + F and H + E) that are both supplementary.

Two angles that are opposite each other as D and B in the figure above are called vertical angles. Vertical angles are always congruent.

$$\angle A\; \angle F\; \angle G\; \angle D\;are\; exterior\; angles\\ \angle B\; \angle E\; \angle H\; \angle C\;are\; interior\; angles\\ \angle B\;and\; \angle E,\; \angle H\;and\; \angle C\;are\; consecutive\; interior\; angles\\ \angle A\;and\; \angle G,\; \angle F\;and\; \angle D\;are\; alternate\; exterior\; angles\\ \angle E\;and\; \angle C,\; \angle H\;and\; \angle B\;are\; alternate\;interior\; angles\\ \left.\begin{matrix} \angle A\;and\; \angle E,\; \angle C\;and\; \angle G\\ \angle D\;and\; \angle H,\; \angle F\;and\; \angle B\\ \end{matrix}\right\} \;are\; corresponding\; angles$$

Two lines are perpendicular if they intersect in a right angle. The axes of a coordinate plane is an example of two perpendicular lines.

In algebra 2 we have learnt how to find the slope of a line. Two parallel lines have always the same slope and two lines are perpendicular if the product of their slope is -1.