Studied by 3 peopleSimilarity
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.
Note
Flashcard