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Parallel Lines, and Pairs of Angles 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:
- Alternate Interior Angles
Learn about Alternate Interior Angles: When two lines are...
- Corresponding Angles
When the two lines being crossed are Parallel Lines the...
- Vertical Angles
Vertical Angles are the angles opposite each other when two...
- Alternate Exterior Angles
Learn about Alternate Exterior Angles: When two lines are...
- 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
They don't have to point in the same direction. They don't...
- Parallel Lines Definition
Lines on a plane that never meet. They are always the same...
- Alternate Interior Angles
where $$$ m_1 $$$ and $$$ m_2 $$$ are the slopes of the two parallel lines. For example, let's consider let's consider a line $$$ \mathit{M_1} $$$ with the equation $$$ y=3x-2 $$$. Its slope is $$$ 3 $$$. For a line $$$ \mathit{M_2} $$$ to be parallel to $$$ \mathit{M_1} $$$ it must have the slope equal to $$$ 3 $$$.
Theorem \(\PageIndex{3}\):The "C" Theorem. If two lines are parallel then the interior angles on the same side of the transversal are supplementary (they add uP to \(180^{\circ}\)). If the interior angles of two lines on the same side of the transversal are supplementary then the lines must be parallel.
- Perpendicular Lines
- Quick Check of Perpendicular
- Vertical Lines
- Summary
Two lines are perpendicular when they meet at a right angle (90°). To find a perpendicular slope: In other words the negative reciprocal
When we multiply a slope m by its perpendicular slope −1m we get simply −1. So to quickly check if two lines are perpendicular: Like this:
The previous methods work nicely except for a vertical line: In this case the gradient is undefined (as we cannot divide by 0): m = yA − yBxA − xB = 4 − 12 − 2 = 30= undefined So just rely on the fact that: 1. a vertical line is parallel to another vertical line. 2. a vertical line is perpendicular to a horizontal line (and vice versa).
parallel lines: sameslopeperpendicular lines: negative reciprocalslope (−1/m)- Slope
- −0.5
Jan 18, 2024 · Plug the coordinates of point P into the equation of your new line to determine b: y₀ = ax₀ + b. 6 = 3 × 1 + b. b = 6 - 3 × 1 = 3. Knowing the values of the slope and y-intercept, you can now write down the full equation of the new line: y = 3x + 3. You can also calculate the distance between the two lines: D = |b - r| / √(m² + 1)
Sep 2, 2024 · Through the point \((6, −1)\) we found a parallel line, \(y=\frac{1}{2}x−4\), shown dashed. Notice that the slope is the same as the given line, but the \(y\)-intercept is different. If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem.
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Nov 28, 2020 · What about the relationship between the slopes of the two lines? Figure 4.6.1.3. To find the slope of line A, we pick two points on the line and draw the blue (upper) right triangle. The legs of the triangle represent the rise and the run. We can see that the slope is 8/4, or 2.
