Parallel & perpendicular lines | Basic geometry (video) | Khan Academy
Two lines that meet in a point are called intersecting lines. A part of a line that has defined endpoints is called a line segment. A line segment as the segment. Lines Rays Angle multicolor title image A line is a collection of points along a straight path that goes on and on in opposite directions. A line has Line segment image An angle is two lines that meet at an endpoint called a vertex. An angle can be named by the three letters that form it or by the letter that is at its vertex. and Lines. Example showing several line segments and their labels Closely related to the line are rays and line segments. If two segments or lines meet at a 90 degree angle we say they are B is called the vertex.
For lack of a better word, a straight line. But why we call it a segment is that it actually has a starting and a stopping point. So, most of the lines that we experience in our everyday reality are actually line segments when we think of it from a pure geometrical point of view. The segment is based on the fact that it has an ending point and a starting point, or a starting point and an ending point.
Lines, Rays, and Angles
A line, if you're thinking about it in the pure geometric sense of a line, is essentially, it does not stop. It doesn't have a starting point and an ending point.
It keeps going on forever in both directions. So a line would look like this.
Lines: Intersecting, Perpendicular, Parallel
And to show that it keeps on going on forever in that direction right over there, we draw this arrow, and to keep showing that it goes on forever in kind of the down left direction, we draw this arrow right over here.
So obviously, I've never encountered something that just keeps on going straight forever. But in math-- that's the neat thing about math-- we can think about these abstract notions.
And so the mathematical purest geometric sense of a line is this straight thing that goes on forever. Now, a ray is something in between. A ray has a well defined starting point. So that's its starting point, but then it just keeps on going on forever.
So the ray might start over here, but then it just keeps on going.
So that right over there is a ray. Now, with that out of the way, let's actually try to do the Khan Academy module on recognizing the difference between line segments, lines, and rays. And I think you'll find it pretty straightforward based on our little classification right over here.
So, let me get the module going. Where did I put it? So what is this thing right over here?Math Antics - Points, Lines, & Planes
Well, it has two arrows on both ends, so it's implying that it goes on forever. So this is going to be a line. The foot is not necessarily at the bottom. More precisely, let A be a point and m a line.
- Lines, line segments, and rays review
- Parallel & perpendicular lines
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.
An introduction to geometry (Geometry, Points, Lines, Planes and Angles) – Mathplanet
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.
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.
Lines, Line Segments, Rays and Angles - ppt video online download
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.
That is the point at which a segment from it to the given point is perpendicular to the line.