Geometry Unit 9

If Carlos ran 100 meters in 15 seconds, how long would it take him to run 44 meters?

6.6 seconds

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

AA Similarity Postulate

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Converse of the Δ Proportionality Theorem

If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.

Corollary 1 of the Δ Proportionality Theorem

If one transversal intersects three or more parallel lines so that it is divided into congruent segments, then any transversal that intersects the same parallel lines will be divided into congruent segments.

Corollary 2 of the Δ Proportionality Theorem

In a proportion, the product of the means is equal to the product of the extremes.

Means-Extremes

______ of rotational symmetry is the number of times an image can coincide with its preimage as it rotates through 360°.

Order

A polygon is similar to itself.

Reflexive

If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.

SAS Similarity Theorem

If the measures of the three sides of one triangle are proportional to the measures of the corresponding three sides of another triangle, then the triangles are similar.

SSS Similarity Theorem

____ polygons are polygons whose corresponding angles are congruent and whose corresponding sides are proportional.

Similar

If one polygon is similar to a second polygon, then the second polygon is similar to the first polygon.

Symmetric

If one polygon is similar to a second polygon, and the second polygon is similar to a third polygon, then the first polygon is also similar to the third polygon.

Transitive

A _____ is a noncongruent transformation in which the size, but not the shape of a geometric figure is changed.

dilation

The first and last terms in a proportion are called the _____.

extremes

A _____ is the composition of transformations that results when a translation is followed by a reflection across a line parallel to the translation vector.

glide reflection

Symmetry is the property of a geometric figure such that when the figure is transformed, the _____ coincides with the preimage.

image

The second and third terms in a proportion are called the _____.

means

A translation is a congruent transformation along a vector such that each segment joining a _____ and its image has the same length as the vector and is parallel to the vector.

point

Angle of rotational symmetry is the smallest angle through which a _____ can be rotated to coincide with its image.

preimage

A _____ is an equation that states that two ratios are equal.

proportion

A _____ is a relationship between two similar quantities.

ratio

A _____ is the ratio of any linear measurement of the image to the corresponding measurement of the preimage in a dilation.

scale factor

A physical representation of an object to the size of the actual object is called a _____.

scale model

The _____ is the ratio of the size of a model of an object to the size of the actual object.

scale ratio

A _____ transformation is a noncongruent transformation in which the points on a given line in a geometric figure remain fixed while other points of the figure are shifted parallel to the line by a distance proportional to their perpendicular distance from the line.

shear

The ____ ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.

similarity

A _____ is a repeating pattern that completely covers a plane with no gaps or overlaps.

tessellation

A quantity that has both length and direction is called a(n) _____.

vector

If a line parallel to one side of a triangle intersects the other two sides, then it divides those two sides proportionally.

Δ Proportionality Theorem