Geometry unit test 6

Similarity

Objects that have the same shape includes: proportional sides and same angles have the _____.

Dilation

A transformation that grows/shrinks a figure, but keep the same overall shape (preserve angles).

Scale factor

When the scale is less than 1, the image is smaller than the pre-image; when the scale is more than 1 then the image is larger than the pre-image. This is the _____.

Similarity transformation

The shape of the figure is retained during dilation.

Colinear

Lies on the same straight line or in a single line.

Rigid transformation

A transformation that preseves length.

Angle-Angle

When two triangles have 2 congruent pairs of angles.

Side-Angle-Side

When two sides are proportional and the included angles are congruent.

Side-Side-Side

When three sides of one triangle are proportional to three sides of another triangle.

Pythagorean theorem

The square of two legs in a triangle equal to the square of the hypotenuse.

Triangle proportionality theorem

A line parallel to one side of a triangle divides the other two sides of the triangle proportionality.

Triangle bisector theorem

The angle bisector of one angle of a triangle divides the opposite side of the triangle into segments proportional to the lengths of the other two sides of the triangles.

opposite/adjacent

Tangent ratio

opposite/hypotenuse

Sine ratio

adjacent/hypotenuse

Cosine ratio

SinA = CosB

The sine of an angle is equal to the cosine of its complementary angle.

CosA = SinB

The cosine of an angle is equal to the sine of its complementary angle.

adjacent/opposite

ArcTan

hypotenuse/opposite

ArcSin

hypotenuse/adjacent

ArcCos

Sin a / a = Sin b / b = Sin c / c

Law of Sines

a^2 + b^2 - 2abcosC = c^2

Law of Cosines

1/2 x ab x sinC

Area of a triangle using sines of an angle.

1 /3 2

30 - 60 - 90 similarity

1 1 /2

45 - 45 - 90 similarity

corresponding angles; corresponding sides

Similar figures will have ___ that are the same measure and ___ that are proportional.