Geometry Chapter 3 Vocabulary

Proportional Equation

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

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.

Similar

Two shapes are ____ if they have exactly the same shape but are not necessarily the same size. ____ polygons have congruent angles, but not congruent sides - the corresponding sides are proportional. The symbol for ______ is ~ .

Congruent

Two shapes are ______ if they have exactly the same shape and size. ________ shapes are similar and have a scale factor of 1. The symbol for this is = with a ~ on top.

Ratio

A ____ compares two quantities by division. A ____ can be written using a colon, but is more often written as a fraction.

Flowchart

A diagram showing an argument for a conclusion from certain evidence. A ___ 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 ____ 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 determine which sides and angles correspond to each other.

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."

Dilation

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

Angle

A(n) _____ is formed by two rays joined at a common endpoint. ____ in geometric figures are usually formed by two segments, with a common endpoint.

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.

Similarity Transformation

Movements of figures that preserve their shape, but not necessarily their size; EX.) reflections, rotations, translations, and dilations

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 ____ ____ are congruent to each other.

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.

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 ______.

Vertex

a point where two or more line segments or rays meet to form a "corner," such as in a polygon or angle

Relationship

a way that two objects (such as two line segments or two triangles) are connected; ______s can be described in two ways: a geometric _______ (such as a pair of vertical angles or two line segments that are parallel), and a ________ between the measures (such as two angles that are complementary or two sides of a triangle that have the same length)