Do Dilations Take Parallel Lines To Parallel Lines?

Are dilations congruent or similar?

In order for two figures to be similar, they must have congruent (equal) corresponding angle measures and proportional sides.

Dilations create similar figures because multiplying by the scale factor creates proportional sides while leaving the angle measure and the shape the same..

Does dilating a triangle change the angles and side length?

While they scale distances between points, dilations do not change angles. While x and y coordinates have not been given to the vertices of the triangle, the coordinate grid serves the same purpose for the given centers of dilation.

Do dilations map angles to Rays?

It splits the sides of ∆ proportionally. O P Q Ps Qs Page 2 MOD2 L8-13 2 Through similar construction, we can show that dilations map rays to rays, lines to lines, circles to circles, and angles to angles. Dilate ray ⃗⃗⃗⃗⃗ by a scale factor of 2 from center O.

How do you center a dilation at a point?

First translate the center of the dilation so the origin becomes the center. Subtracting the coordinate values of the center of dilation will move the center to the origin. Given center of dilation at (a,b), translate the center to (0,0): (x – a, y – b).

Are all angles in similar figures congruent?

In similar figures, the angles are congruent, even if the sides are not. Notice that one angle in each pair of figures corresponds to an angle in the other figure. They have the same shape but not the same size.

Are dilations always parallel?

When you dilate a line segment, the original line segment will always be parallel to (or on the same line as) the image.

What are perpendicular lines?

Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

How do you dilate a circle on a graph?

Dilation To dilate a circle, we start with our standard equation: x2+y2=r2 To dilate the circle we multiply our desired factor squared into the right side of the equation. For example, two multiply the diameter of the circle by two, our equation would now be x2+y2=22(r2).

Do dilations always increase the length of the line segments?

While they scale distances between points, dilations do not change angles. Transformations affect all points in the plane, not just the particular figures we choose to analyze when working with transformations.

How can you tell if triangles are similar?

If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

What does congruent mean in math?

Congruent means same shape and same size. So congruent has to do with comparing two figures, and equivalent means two expressions are equal. So to say two line segments are congruent relates to the measures of the two lines are equal.

What are the properties of dilations?

Dilations map lines to lines, rays to rays, and segments to segments. Dilations map angles to angles of the same degree. Dilations map lines to lines, rays to rays, and segments to segments. Dilations map angles to angles of the same degree.

Do dilations take perpendicular lines to perpendicular lines?

Dilations take perpendicular lines to perpendicular lines. Dilations of an angle are congruent to the original angle.

Do dilations map lines to lines?

DILATION THEOREM FOR RAYS: A dilation maps a ray to a ray sending the endpoint to the endpoint. scale factor �� of the dilation is equal to 1, then the dilation maps the line to the same line. Otherwise, the dilation maps the line to a parallel line.

Is it true that dilations increase the measure of angles?

A dilation with a scale factor greater than 1, such as the dilation above, is an enlargement. A dilation with a scale factor less than 1 but greater than 0 is a reduction. So, in general, a dilation either enlarges or reduces the size of a figure but does not change the measure of the angles.

Is it true dilations of a triangle are congruent to the original triangle?

Dilations of a triangle are not congruent but similar to the original triangle. Dilations does not increase the measure of angles, instead it keeps the angle measure. Dilations does not always increase the length of line segments, it an either increase or decrease the length.

How do you find the scale factor of two lines?

To find a scale factor between two similar figures, find two corresponding sides and write the ratio of the two sides. If you begin with the smaller figure, your scale factor will be less than one. If you begin with the larger figure, your scale factor will be greater than one.