# Perpendicular lines meet at right angles

### Parallel and perpendicular lines review (article) | Khan Academy

"The line with the equation 3x + by = 6 intersects with the line 6y + ax = c at right Two lines on a graph that meet at right angles are perpendicular to each other . In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). Identify and draw parallel and perpendicular lines in some practice problems. lines}} Perpendicular lines are lines that meet at right angles. same distance apart from each other — no matter how far they are extended, they will never meet.

## Parallel & perpendicular lines

And just as a reminder, two lines are parallel if they're in the same plane, and all of these lines are clearly in the same plane. They're in the plane of the screen you're viewing right now.

But they are two lines that are in the same plane that never intersect.

And one way to verify, because you can sometimes-- it looks like two lines won't intersect, but you can't just always assume based on how it looks. You really have to have some information given in the diagram or the problem that tells you that they are definitely parallel, that they're definitely never going to intersect.

And one of those pieces of information which they give right over here is that they show that line ST and line UV, they both intersect line CD at the exact same angle, at this angle right here. And in particular, it's at a right angle.

And if you have two lines that intersect a third line at the same angle-- so these are actually called corresponding angles and they're the same-- if you have two of these corresponding angles the same, then these two lines are parallel. So line ST is parallel to line UV. And we can write it like this. Line ST, we put the arrows on each end of that top bar to say that this is a line, not just a line segment.

### Angles and Perpendicular Lines ( Read ) | Geometry | CK Foundation

Line ST is parallel to line UV. And I think that's the only set of parallel lines in this diagram. Now let's think about perpendicular lines. Perpendicular lines are lines that intersect at a degree angle. So, for example, line ST is perpendicular to line CD. So line ST is perpendicular to line CD. The diagram can be in any orientation.

## Lines: Intersecting, Perpendicular, Parallel

The foot is not necessarily at the bottom. More precisely, let A be a point and m a line. If B is the point of intersection of m and the unique line through A that is perpendicular to m, then B is called the foot of this perpendicular through A. Construction of the perpendicular[ edit ] Construction of the perpendicular blue to the line AB through the point P. Construction of the perpendicular to the half-line h from the point P applicable not only at the end point A, M is freely selectableanimation at the end with pause 10 s To make the perpendicular to the line AB through the point P using compass-and-straightedge constructionproceed as follows see figure left: Let Q and P be the points of intersection of these two circles.

Perpendicular Lines, Slope, Rays, Segments & Right Angles - Geometry Practice Problems

To make the perpendicular to the line g at or through the point P using Thales's theoremsee the animation at right. The Pythagorean theorem can be used as the basis of methods of constructing right angles.

For example, by counting links, three pieces of chain can be made with lengths in the ratio 3: These can be laid out to form a triangle, which will have a right angle opposite its longest side.

This method is useful for laying out gardens and fields, where the dimensions are large, and great accuracy is not needed. The chains can be used repeatedly whenever required. In relationship to parallel lines[ edit ] The arrowhead marks indicate that the lines a and b, cut by the transversal line c, are parallel. If two lines a and b are both perpendicular to a third line call of the angles formed along the third line are right angles. Therefore, in Euclidean geometryany two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate.

Conversely, if one line is perpendicular to a second line, it is also perpendicular to any line parallel to that second line.

In the figure at the right, all of the orange-shaded angles are congruent to each other and all of the green-shaded angles are congruent to each other, because vertical angles are congruent and alternate interior angles formed by a transversal cutting parallel lines are congruent. Therefore, if lines a and b are parallel, any of the following conclusions leads to all of the others: One of the angles in the diagram is a right angle.

One of the orange-shaded angles is congruent to one of the green-shaded angles. Line c is perpendicular to line a. Line c is perpendicular to line b.

In computing distances[ edit ] The distance from a point to a line is the distance to the nearest point on that line.