Chapters 7-8 Flashcards
an equation stating tat two ratios are equal is called this
proportion
a comparison of two quantities using division
ratio
Ex: a/b=c/d
a and d are
extremes
ex:a/b=c/d
b and c are
means
ex: a/b=c/d
the product of the extremes ad and the product of the means bc
cross products
polygons that have the same shape but not necessarily the same size
similar polygons
the ratio of the lengths of the corresponding sides of two similar polygons is
scale factor
a segment with endpoints that are the midpoints of two sides of the triangle
*every triangle has three
midsegment of a triangle
an angle bisector in a triangle separates the opposite side into two segments that are proportional to the lengths of the other two sides
triangle angle bisector
a transformation that enlarges or reduces the original figure proportionally
dilation
a dilation is a type of ____________
similarity transformation
a dilation with a scale factor greater than 1 produces this
enlargement
a dilation with a scale factor between 0 and 1 produces this
reduction
an object or drawing with lengths proportional to the object it represents
scale model or a scale drawing
the ratio of a length on the model or drawing to the actual ength f the object being modeled or drawn
scale
comes from two Greek terms, trigon, meaning triangle, and metron, meaning measure
trigonometry
a ratio of the lengths of two sides of a right triangle
trigonometric ratio
the ratio of he length of the leg opposite the angle to the length of the hypotenuse
sine
the ratio of the length of the leg adjacent the angle to the length of the hypotenuse
cosine
the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle
tangent
if angle A is an acute angle and the sine of A is x, the the _________ of x is the measure of angle A
inverse sine
if angle A is an acute angle and the cosine of A is x, then the ___________ of x is the measure of angle A
inverse cosine
if angle A is an acute angle and the tangent of A is x, then the __________ of x is the measure of angle A
inverse tangent
the angles formed by a horizontal line and an observer’s line of sight to an objet above the horizontal line
angle of elevation
the angle formed by a horizontal line and an observer’s line of sight to an object below the horizontal line
angle of depression
can be used to find side lengths and angle measures for any triangle
Law of Sines
used to solve a triangle if you know the measures of two sides and the included angle (SAS)
Law of Cosines
describes both the magnitude and direction of the quantity
vector
the length of the vector fro its initial point to its terminal point
magnitude
can be expressed as the angle that it forms with the horizontal or as a measurement between 0 degrees and 90 degrees east or west of the north-south
direction
sum of two or more vectors is a single vector called this
resultant
a vector is in this position if its initial point is at the origin
standard position
used to describe a vector with any initial point, you can use this form or x, y (with brackets)
component form
