Topic 7: Dilations and Similarity

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape. It involves a center point and a scale factor.

Front

What does it mean for two triangles to be similar?

Back

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

Front

What is the AA similarity criterion?

Back

The AA (Angle-Angle) similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What is the SSS similarity criterion?

Back

The SSS (Side-Side-Side) similarity criterion states that if the lengths of the corresponding sides of two triangles are proportional, the triangles are similar.

Front

What is the SAS similarity criterion?

Back

The SAS (Side-Angle-Side) similarity criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

How do you write a similarity statement for triangles?

Back

A similarity statement indicates that two triangles are similar, using the notation ΔABC ~ ΔDEF, where corresponding vertices are in the same order.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

If the scale factor of a dilation is 2, what happens to the dimensions of the original figure?

Back

If the scale factor is 2, each dimension of the original figure is multiplied by 2, making the figure twice as large.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

Front

If triangle XYZ has sides of lengths 3, 4, and 5, and triangle ABC is similar to it with a scale factor of 3, what are the lengths of the sides of triangle ABC?

Back

The lengths of the sides of triangle ABC are 9, 12, and 15.