Search results
storyofmathematics.com
- Alternate Angles a and b: ∠a and ∠b are alternate interior angles. Since ∠a = 60° and ∠b = 60°, they are equal. Therefore, lines a and b are parallel.
www.bytelearn.com/math-topics/parallel-lines
Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember: Always the same distance apart and never touching. The red line is parallel to the blue line in each of these examples: Parallel lines also point in the same direction. Parallel lines have so much in common.
- Alternate Interior Angles
To help you remember: the angle pairs are on Alternate sides...
- Corresponding Angles
Parallel Lines. When the two lines being crossed are...
- Vertical Angles
Notice how the 4 angles are actually two pairs of "vertical...
- Alternate Exterior Angles
To help you remember: the angle pairs are on Alternate sides...
- Line in Geometry
Ray. When it has just one end it is called a "Ray". This is...
- Consecutive Interior Angles
To help you remember: the angle pairs are Consecutive (they...
- Congruent Angles
Congruent - why such a funny word that basically means...
- Parallel Lines Definition
Lines on a plane that never meet. They are always the same...
- Alternate Interior Angles
- Overview
- Comparing the Slopes of Each Line
- Using the Slope-Intercept Formula
- Defining a Parallel Line with the Point-Slope Equation
Parallel lines are two lines in a plane that will never intersect (meaning they will continue on forever without ever touching).
A key feature of parallel lines is that they have identical slopes.
The slope of a line is defined as the rise (change in Y coordinates) over the run (change in X coordinates) of a line, in other words how steep the line is.
Parallel lines are most commonly represented by two vertical lines (ll). For example, ABllCD indicates that line AB is parallel to CD.
Define the formula for slope.
The slope of a line is defined by (Y
) where X and Y are the horizontal and vertical coordinates of points on the line. You must define two points on the line to calculate this formula. The point closer to the bottom of the line is (X
) and the point higher on the line, above the first point, is (X
This formula can be restated as the rise over the run. It is the change in vertical difference over the change in horizontal difference, or the steepness of the line.
If a line points upwards to the right, it will have a positive slope.
Define the slope-intercept formula of a line.
The formula of a line in slope-intercept form is y = mx + b, where m is the slope, b is the y-intercept, and x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation. In this form, you can easily determine the slope of the line as the variable "m".
For example. Rewrite 4y - 12x = 20 and y = 3x -1. The equation 4y - 12x = 20 needs to be rewritten with algebra while y = 3x -1 is already in slope-intercept form and does not need to be rearranged.
Rewrite the formula of the line in slope-intercept form.
Oftentimes, the formula of the line you are given will not be in slope-intercept form. It only takes a little math and rearranging of variables to get it into slope-intercept.
For example: Rewrite line 4y-12x=20 into slope-intercept form.
Point-slope form allows you to write the equation of a line when you know its slope and have an (x, y) coordinate. You would use this formula when you want to define a second parallel line to an already given line with a defined slope. The formula is y – y
= m (x – x
) where m is the slope of the line, x
is the x coordinate of a point given on the line and y
is the y coordinate of that point.
As in the slope-intercept equation, x and y are variables that represent coordinates on the line; generally, you will see them remain as x and y in the equation.
- 223K
Sep 5, 2021 · \(\overleftrightarrow{AB} || \overleftrightarrow{CD}\) since the arrows indicate parallel lines. \(x^{\circ} = 40^{\circ}\) because alternate interior angles of parallel lines are equal. \(y^{\circ} = z^{\circ} = 180^{\circ} - 40^{\circ} = 140^{\circ}\). Answer: \(x = 40, y = 140, z = 140\).
How do we know when two lines are parallel? Their slopes are the same! The slope is the value m in the equation of a line: y = mx + b. Example: Find the equation of the line that is: parallel to y = 2x + 1. and passes though the point (5,4) The slope of y = 2x + 1 is 2. The parallel line needs to have the same slope of 2.
- Slope
- −0.5
Jun 4, 2024 · In the diagram, parallel lines are shown in two ways, Line A is parallel to Line B, and Line X is parallel to Line Y. Parallel Lines Definition. Parallel lines are the lines in a plane that never cross or intersect at any point, remaining constantly equidistant from one another. Parallel Lines Symbol.
If two lines are parallel to the same line, they are parallel to each other. Parallel lines cut by a transversal have the following properties: Corresponding angles are congruent.
When a transversal intersects two parallel lines, it creates a set of angles like: corresponding angles, alternate interior angles and alternate exterior angles. Understanding the properties of transversal lines and the angles they create is essential to solving many geometry problems and applying these concepts in practical, real-life situations.
