Topic 6: Geometry Transformations and Triangle Angles

Vocabulary flashcards covering geometric transformations (translations, reflections, rotations, dilations), congruency, similarity, and triangle angle theorems.

Alternate interior angles

Angles that lie within a pair of lines and on opposite sides of a transversal.

Same-side interior angles

Angles that lie within a pair of lines and on the same side of a transversal.

Corresponding angles

Angles that lie on the same side of the transversal and in corresponding positions.

Exterior angle of a triangle

An angle formed by a side and an extension of an adjacent side of a triangle.

Remote interior angles of a triangle

Two interior angles that correspond to each exterior angle of a triangle (note: the measure of an exterior angle is equal to the sum of these angles).

Translation

A transformation that maps each point of the preimage the same distance and in the same direction.

Reflection

A transformation where figures are the same distance from the line of reflection but on opposite sides.

Rotation

A transformation that turns a figure about a fixed point called the center of rotation.

Angle of rotation

The number of degrees a figure is rotated about its center of rotation.

Compose a sequence of transformations

To perform one transformation and then use the resulting image to perform the next transformation.

Congruent figures

Two figures that are identical in shape and size because a sequence of transformations maps one figure onto the other.

Dilation

A transformation that results in an image that is the same shape but not the same size as the preimage.

Similar figures

Figures that have the same shape, congruent angles, and proportional side lengths, where one can be mapped to the other via translations, reflections, rotations, and dilations.

Interior angles of a triangle sum

The sum of the measures of the interior angles of a triangle is always $180^{\circ}$.

AA Criterion (Angle-Angle Triangle Similarity)

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

Reflection across the y-axis rule

The transformation rule $(x, y) \rightarrow (-x, y)$.

$90^{\circ}$ rotation about the origin rule

The transformation rule $(x, y) \rightarrow (-y, x)$.