Geometry-Chapter 3 Vocabulary

Similarity Statement

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

Corresponding Sides

Sides in two or more figures that are images of each other with respect to a sequence of transformations. If two figures are congruent, their corresponding sides are congruent to each other.

Flowchart

A diagram showing an argument for a conclusion from certain evidence. A flowchart uses ovals connected by arrows to show the logical structure of the argument. When each oval has a reason stated next to it showing how the evidence leads to that conclusion, the flowchart represents a proof.

Dilation

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

Congruent

Two shapes are congruent if they have exactly the same shape and size. Congruent shapes are similar and have a scale factor of 1.

Relationship

a way that two objects (such as two line segments or two triangles) are connected

Translate

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). Note that a translation is sometimes referred to as a "slide."

Proportional Equation

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

Vertex

For a two-dimensional geometric shape, a vertex is a 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 vertex is a point where the edges of the solid meet.

Angle Angle Triangle Similarity (AA ~)

If two angles of one triangle are congruent to the two corresponding angles of another triangle, then the triangles are similar. For example, given ΔABC and ΔA'B'C' with ∠A ≅ ∠A' and ∠B ≅ ∠B', then ΔABC ~ ΔA'B'C'. 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, then the triangles are similar.

Angle

In general, an angle is formed by two rays joined at a common endpoint. Angles in geometric figures are usually formed by two segments, with a common endpoint

Similarity Transformation

Movements of figures that preserve their shape, but not necessarily their size. Examples of similarity transformations are reflections, rotations, translations, and dilations.

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).

Perimeter

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

Hypotenuse

The longest side of a right triangle (the side opposite the right angle). Note that legs of a right triangle are always shorter than its hypotenuse

Similar

Two shapes are similar if they have exactly the same shape but are not necessarily the same size. Similar polygons have congruent angles, but not congruent sides - the corresponding sides are proportional.

Ratio

compares two quantities by division. A ratio can be written using a colon, but is more often written as a fraction. For example, in the two similar triangles below, a ratio can be used to compare the length of in ΔABC with the length of in ΔDEF. This ratio can be written as 5:11 or as the fraction .