Chapter 3: Justification and Similarity

Corresponding Sides

Sides in two or more figures that are images of each other with respect to a transformation.

Flowchart

A diagram showing an argument for a conclusion from certain evidence. Uses ovals connected by arrows to show the logical structure of the argument.

Logical Argument

A logical sequence of statements and reasons that lead to a conclusion. Can be written in a paragraph, represented with a flowchart, or documented in a two-column proof.

Statement

A recording of fact to present evidence in a logical argument.

Dilation

A transformation which produces a figure similar to the original by proportionally shrinking or stretching the figure. A shape is stretched or compressed proportionally from a point.

Relationship

A way that two objects are connected.

Proportional Equation

An equation stating that two ratios are equal.

Similar Figures

IF two shapes have exactly the same shape but are not necessarily the same size.

AA~ (Triangle Similarity)

If two angles of one triangle are congruent to the two corresponding angles of another triangle, then the triangles are similar.

Congruent

If two shapes have exactly the same shape (similar) and size (have a scale factor of 1).

SSS~ (Triangle Similarity)

If two triangles have all three pairs of corresponding sides that are proportional (this means that the ratios of corresponding sides are equal), then the triangles are similar.

SAS~ (Triangle Similarity)

If two triangles have two pairs of corresponding sides that are proportional and have congruent included angles then the triangles are similar.

Zoom Factor

The amount each side of a figure is multiplied by when the figure is proportionally enlarged or reduced in size. It is written as the ratio of a length in the new figure (image) to a length in the original figure (preimage)

Enlarge

To increase in size.