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Geometry Module 2

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12 cards

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Section 1

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Dilation

Front

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Geometry Math

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7 years ago

Date created

Mar 1, 2020

Cards (12)

Section 1

(12 cards)

Dilation

Front

For r>0, a dilation with center C and scale factor r is a transformation D_(C,r) of the plane defined as follows: For the center C, D_(C,r) (C)=C, and For any other point P, D_(C,r) (P) is the point Q on (CP) ⃗ so that CQ=r∙CP.

Back

Slope

Front

The ratio of the rise and the run between any two points in a line

Back

Sides of a Right Triangle

Front

The hypotenuse of a right triangle is the side opposite the right angle; the other two sides of the right triangle are called the legs. Let θ be the angle measure of an acute angle of the right triangle. The opposite side is the leg opposite that angle. The adjacent side is the leg that is contained in one of the two rays of that angle.

Back

Similar

Front

Two figures in a plane are similar if there exists a similarity transformation taking one figure onto the other figure. A congruence is a similarity with scale factor 1. It can be shown that a similarity with scale factor 1 is a congruence.

Back

Scale drawing

Front

Is a drawing that is similar to an actual object, or place. Floor plans, blue prints, and maps are all examples of scale drawings.

Back

Similarity Transformation

Front

A similarity transformation (or similarity) is a composition of a finite number of dilations or basic rigid motions. The scale factor of a similarity transformation is the product of the scale factors of the dilations in the composition; if there are no dilations in the composition, the scale factor is defined to be 1. A similarity is an example of a transformation.

Back

Cosine

Front

(Let θ be the angle measure of an acute angle of the right triangle. The cosine of θ of a right triangle is the value of the ratio of the length of the adjacent side (denoted adj) to the length of the hypotenuse (denoted hyp). As a formula, cos⁡θ=adj/hyp.)

Back

Rigid motions

Front

transformations that preserve distance and angle

Back

Pythagorean theorem

Front

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs

Back

Sine

Front

Let θ be the angle measure of an acute angle of the right triangle. The sine of θ of a right triangle is the value of the ratio of the length of the opposite side (denoted opp) to the length of the hypotenuse (denoted hyp). As a formula, sin⁡θ=opp/hyp.

Back

Tangent

Front

Let θ be the angle measure of an acute angle of the right triangle. The tangent of θ of a right triangle is the value of the ratio of the length of the opposite side (denoted opp) to the length of the adjacent side (denoted adj). As a formula, tan⁡θ=opp/adj.)

Back

Scale factor

Front

the ratio of corresponding linear measurements of two similar figures

Back