Two lines intersecting at a right angle form a line. are parallel. are perpendicular. form a ray.

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.

When 2 lines intersect at a right angle, they are perpendicular lines. We can also say that if 2 lines are perpendicular, then their intersection forms a right angle. Sometimes in everyday language, parts of lines (rays and line segments) that meet at right angles are also called perpendicular lines.

Lines l and m are perpendicular because they meet at a right angle. We can write l⊥m to show this, where "⊥" is the symbol for perpendicular.

Also, if two lines are perpendicular, 4 right angles are created. In the diagram below, angles 1, 2, 3, 4 are all right angles.

Properties of perpendicular lines

• There can be only one line that is perpendicular to a given line at a given point.

Let lines m, n, and l intersect at point P above. If the angle formed by l and m is a right angle, then the angle formed by lines l and n cannot also be a right angle.

• Two lines are perpendicular if their slopes are negative (or opposite) reciprocals of each other.

The slope of line p is ½ and the slope of line r is -2, the negative reciprocal of ½, so p and q are perpendicular and meet at a right angle.

Knowing that two perpendicular lines meet at a right angle, or that if their intersection forms a right angle that they are perpendicular, is useful information in working with postulates, theorems, and other properties in Geometry. Below are a few examples.

• If the two non-adjacent sides of two acute adjacent angles are perpendicular then, the angles must be complementary.

∠BAD and ∠CAD are adjacent angles, with non-adjacent, perpendicular sides AB and AC. Since AB and AC are perpendicular, ∠BAC is a right angle measuring 90° so, ∠BAD + ∠CAD = 90°.

• If a transversal is perpendicular to one of a pair of parallel lines (or several parallel lines), it must be perpendicular to all the parallel lines.

In the diagram above, m//n and l⊥m. Since l⊥m, all four angles formed by the intersection of l and m are right angles. Also, since m//n all four angles are also right angles formed by lines l and n, by the property of corresponding angles of parallel lines being congruent. Thus, line l is also perpendicular to line n.

Did you know?

The x- and y-axis are two lines in the Cartesian coordinate plane that are perpendicular to each other.

Also, each horizontal grid line is perpendicular to each vertical grid line that comprises the grid for the system. The Cartesian coordinate system is also known as an orthogonal (meaning at right angles) coordinate system.

What is two lines intersecting at a right angle?

When two lines intersect at a right angle then the lines are said to be perpendicular lines?

Are 2 intersecting lines perpendicular?

Which line intersects and is perpendicular to the parallel lines?