Similarity and Dilations

Front

What is similarity in geometry?

Back

Similarity in geometry refers to figures that have the same shape but may differ in size. Corresponding angles are equal, and corresponding sides are in proportion.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape. It is defined by a center point and a scale factor.

Front

What does a scale factor of 2 mean in dilation?

Back

A scale factor of 2 means that the figure will be enlarged to twice its original size.

Front

What does a scale factor of 1/2 mean in dilation?

Back

A scale factor of 1/2 means that the figure will be reduced to half its original size.

Front

How do you find the coordinates of a point after dilation?

Back

To find the coordinates after dilation, multiply the original coordinates by the scale factor. For example, if the original point is (x, y) and the scale factor is k, the new coordinates will be (kx, ky).

Front

What is the relationship between corresponding sides of similar triangles?

Back

In similar triangles, the lengths of corresponding sides are proportional. If triangle A is similar to triangle B, then AB/BC = A'B'/B'C'.

Front

If triangle ABC is dilated by a scale factor of 3, what happens to its area?

Back

The area of triangle ABC will be multiplied by the square of the scale factor. If the scale factor is 3, the area will increase by a factor of 3^2 = 9.

Front

What is the formula for finding the area of a triangle?

Back

The area of a triangle can be found using the formula: Area = 1/2 * base * height.

Front

What is the effect of dilation on angles?

Back

Dilation does not change the measures of angles. The angles remain congruent before and after the dilation.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.