Geometry Chapter 3 Vocabulary

Corresponding Sides

Sides in two or more figures that are images of each other with respect to sequence of transformations. If tow figures are congruent, then these parts of them are congruent to each other.

Similarity Transformations

Movements of figures that preserve their shape, but not necessarily their size. These include reflections, rotations, translations, and dilations.

Vertex

(A) For a two dimensional geometric shape, the point where two or more line segments or rays meet to form a "corner," such as in a polygon or angle. (B) For a three-dimensional polyhedron, a point where the edges of the solid meet. (C) On a graph, the lowest or highest point of the graph of a parabola or absolute value function, depending on the graph's orientation.

Ratio

A comparisons of two quantities by division. IT can be written with a colon, but more commonly as a fraction.

Flowchart

A diagram showing an argument for a conclusion fro certain evidence. This uses ovals connected by arrows to show the logical structure of the argument. When each oval has a reason showing how the evidence leas to that conclusion, this represents a proof.

Similarity Statement

A statement that indicates that two figures are similar. The order of the letters in the names of the shapes in this statement indicates which sides and angels correspond to each other.

Translation

A transformation that preserves the size, shape, and orientation of a figure while sliding (moving) it to a new location. The result is called the image of the original figure (preimage). Often called a "slide".

Dilation

A transformation which produces a figure similar to the original by shrinking or stretching the figure. In one of these, the shape is stretched (or compressed) proportionally from a point, called the point of dilation.

Proportional Equation

An equation stating that two ratios are equal. These are a useful type of equation to set up when solving problems involving proportional relationships.

Angle Angle Triangle Similarity (AA ~)

If tow angles of one triangle are congruent to the two corresponding angles of another triangle, then the triangles are similar. You can also show that two triangles are similar by showing that three pairs of corresponding angles are congruent (Which would be called AAA ~), but two pairs of angles are sufficient to demonstrate similarity.

Side Side Side Triangle Similarity (SSS ~)

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.

Side Angle Side Triangle Similarity (SAS ~)

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

Angle

In general, formed by two rays joined at a common endpoint. In geometric figures, these are usually formed by two segments, with a comment endpoint.

Zoom Factor

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

Perimeter

The distance around the exterior of a figure on a flat surface. For a polygon, this is the sum of the lengths of its sides. Also called circumference for a circle.

Hypotenuse

The side of a right triangle opposite the right angle. The legs of a right triangle are always shorter than the hypotenuse of the same triangle.

Relationship

The way that two objects, such as two line segments or two triangles, are connected. When you know the similarities held between two objects, learning about one object can give you information about the other. These have two forms: geometric, such as a pair of vertical angles or two parallel line segments, and measures, tow angels that are complementary or tow sides of a triangle with the same length. Common geometric ones between two figures include being similar (when two figures have the same shape, but not necessarily the same size) and being congruent (when two figures have the same shape and the same size.)

Congruent

Two shapes are this if they have exactly the same shape and size. These shapes are similar and have a scale factor of 1. The symbol for this is ≅.

Similar Figures

Two shapes that have exactly the same shape but are not necessarily the same size. Polygons of this nature have congruent angles, but not necessarily congruent sides. the corresponding sides are proportional. The symbol for this is ~.