Geometry Unit 4 Pre-Test

Front

What is a proportion in geometry?

Back

A proportion is an equation that states that two ratios are equal. For example, if \( \frac{a}{b} = \frac{c}{d} \), then \( a \) is to \( b \) as \( c \) is to \( d \).

Front

How do you solve for a missing value in a proportion?

Back

To solve for a missing value in a proportion, cross-multiply the known values and then isolate the variable. For example, if \( \frac{AB}{BM} = \frac{?}{CD} \), then \( AB \cdot CD = BM \cdot ? \).

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. This can be established using the AA (Angle-Angle) similarity criterion.

Front

What is the AA similarity criterion?

Back

The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then 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 in proportion to two sides of another triangle, and the included angles are equal, then the triangles are similar.

Front

What is the SSS similarity criterion?

Back

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

Front

What is dilation in geometry?

Back

Dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center point and a scale factor.

Front

How do you represent a dilation mathematically?

Back

A dilation can be represented as \( (x, y) \rightarrow (kx, ky) \), where \( k \) is the scale factor.

Front

What is a scale factor in dilation?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a shape. A scale factor greater than 1 enlarges the shape, while a scale factor between 0 and 1 reduces it.

Front

What is the relationship between corresponding sides of similar triangles?

Back

In similar triangles, the lengths of corresponding sides are proportional. If triangle ABC is similar to triangle DEF, then \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \).