Geometry Ch. #7 Vocabulary

image (7.6)

the new figure after the dilation

Symmetric Property of Similarity (7.3)

If Triangle ABC is similar to Triangle DEF, then Triangle DEF is similar to triangle ABC.

Triangle Proportionality Theorem (Divided Sides Theorem) (7.4)

If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally. (If EF is parallel to BC, then AE/BE=AF/FC.)

pre-image (7.6)

the original figure

midsegment triangle (7.4)

the triangle formed by joining all three midsegments of a triangle

Triangle Midsegment Theorem (7.4)

A midsegment of a triangle is parallel to one side of the triangle and equal to half the length of that side.

Transitive Property of Similarity (7.3)

If Triangle ABC is similar to Triangle DEF and Triangle DEF is similar to Triangle XYZ, then Triangle ABC is similar to Triangle XYZ.

Triangle Proportionality Converse (7.4)

If a line divides two sides of a triangle proportionally, then it is parallel to the third side. If AE/BE=AF/FC, then EF is parallel to BC.

SSS for Similar Triangles Theorem (7.3)

If the three sides of one triangle are proportional to the three corresponding sides of a second triangle, then the two triangles are similar.

AA for Similar Triangles Postulate (7.3)

If two angles of one triangle are congruent to two angles of a second triangle, the two triangles are similar.

SAS for Similar Triangles Theorem (7.3)

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.

Triangle Angle Bisector Theorem (7.4)

In a triangle, the angle bisector of an angle divides the opposite side proportional to the other two sides. (If angle BAD is congruent to angle CAD, then BD/DC=AB/AC.

Cross Product Property (7.1)

The product of the extremes equals the product of the means.

Reflexive Property of Similarity (7.3)

Triangle SAS is similar to Triangle SAS.

extended ratio (7.1)

a comparison of three or more quantities. The expression a:b:c means the ratio of the first two quantities is a:b, the ratio of the last two quantities is b:c, and the ratio of the first and last quantities is a:c.

ratio (7.1)

a comparison of two quantities measured in the same unit of measures (must be in simplest form)

rate (7.1)

a comparison of two quantities measures in different units of measures (average rate has a denominator of one)

midsegment of a triangle (7.4)

a segment joining the midpoints of two sides of the triangle. There are 3 midsegments to a triangle.

dilation (7.6)

a transformation that changes size of a figure but not its shape

similarity transformation (7.6)

a transformation that produces a similar figure

proportion (7.1)

an equation of two equal ratios (a compares to b as c compares to d)

Indirect measurement (7.7)

any method that uses formulas, similar figures and/or properties to measure an object.

per (7.1)

for each

The ratio of the areas of two similar figures is the square of the ratio of their (7.7)

linear measures (similarity ratio).

similar polygons (7.2)

polygons that have all of their corresponding angles congruent and all of their corresponding side lengths proportional

scale factor or magnitude (7.6)

the magnitude or amount of change (represented by k)

scale (in a scale drawing) (7.7)

the ratio of any length in the drawing to the corresponding actual length. Ex. 1 cm=1500 m

similarity ratio (constant of proportionality) (7.2)

the ratio that two sets of corresponding sides have ex. AC=1 CB=2 AD=2 DE=4 similarity ratio of AB/CB and AD/DE=1/2

average rate of change (7.1)

Example: 60 miles per 1 hour

Two-Transversal Proportionality Theorem (7.4)

If three or more parallel lines intersect two transversals, then they divide the transversal proportionally. (If AB is parallel to CD which is parallel to EF, then AC/CE= BD/DF.)

scale drawing (7.7)

a drawing which represents an object as smaller or larger than its actual size.

scale factor: 0<k<1 (7.6)

the dilation is a reduction

scale factor: k<0 (7.6)

the dilation is a rotation -1<k<0= reduction+ rotation of 180° k<-1=enlargement+ rotation of 180°

scale factor: k>1 (7.6)

the dilation is an enlargement

center of dilation (7.6)

the fixed point that dilations are performed with respect to

Theorem:Sk is a transformation which maps (x, y) onto . is the scale factor. (7.6)

(kx, ky). k

Properties of proportions (7.1)

-Proportions are equivalent if they have the same cross product equation. -The reciprocals of the ratios in a proportion are also proportional.