M2.M6 Geometry
Pythagorean Triple
5-12-13 6-8-10
Altitude
A line which passes through a vertex of a triangle and meets the opposite side at the right angles
Tangent
A ratio representing the opposite side length divided by the adjacent side length
If A is an acute angle of a 45-45-90 triangle, then cos(A)=cos(90-A). True or False?
True
If A is an acute angle of a right triangle, then cos(A)=sin(90-A). True or False?
True
The acute angles in a right triangle are complementary. True or False?
True
The cosine ratio of a non-right angle of a right triangle is equal to the adjacent side divided by the hypotenuse. True or False?
True
The sine ratio of an acute angle in a right triangle is equal to the cosine ratio of the other acute angle. True or False?
True
The tangent ratio of an acute angle in a right triangle is equal to the reciprocal of the tangent ratio of the other acute angle. True or False?
True
Ratio
a comparison of values
dilation
a transformation in which the preimage reduces or enlarges with respect to a point
Theorem 1: do they want they want the altitude?
altitude equals square root of hypotenuse part 1 times hypotenuse part 2
DIlations with a scale factor of 1 ____ produce congruent figures
always
Parallelograms with all four sides and all four angles congruent are _____ similar
always
Triangles with corresponding congruent angles are ____ similar
always
The distances of corresponding vertices from the ____ of the dilation are ______ to the lengths of corresponding segments.
center, equidistant
Every corresponding preimage point, image point and Center of dilation are always ...
collinear
The angle of ______ should be the angle between your line of sight the line connecting you straight to the object you are view.
depression
A dilation by the scale factor of 1.2 would result in a....
enlargement
K > 1
enlargement
k=1.5
enlargement
A dilation of a figure preserves the lengths of the figure. T/F?
false
SImilar
figures with corresponding angles congruent and corresponding sides proportional
If an altitude is drawn to the _______ of a right triangle, the length of the altitude is the geometric ______ between the lengths of the two _______ formed on the hypotenuse
hypotenuse, mean, segments
To find the scale factor of a dilation, you can divide the length of a segment on the ______ by the length of its corresponding segment on the _____.
image, preimage
distance from the c.o.d to image point/distance from the c.o.d to preimage =?
k (scale factor)
Midsegment
s segment connecting the midpoints of two sides of a triangle
If A is an acute angle of a right triangle, then tan(A)=tan(90-A). True or False?
False only true in 45-45-90 triangles
If given the pre-image and image of a dilation, you can locate the _____ at the intersection of the lines passing through the corresponding points
Center of dilation
All rectangles are similar. True or False?
False
Corresponding angles are complementary. True or False?
False
If a parallelogram has perpendicular diagonals, then the paralleogram is a rectangle. T/F?
False
If both pairs of opposite sides of a quadrilateral have the same slope, then the figure is a rectangle. T/F?
False
Similar figures are never congruent. T/F?
False
The following sets of numbers are Pythagorean Triple: 3,4,5 5,12,13 6,8,15 7,24,25. True or False?
False
If A is an acute angle of a right triangle, then cos(A)=sin(A). True or False?
False only true in 45-45-90 triangles
After a dilation, corresponding segments that are not contained in the same line are ____.
Parallel
If an altitude is drawn to the hypotenuse of a right triangle, then the length of each _____ of the right triangle is the ________ mean between the length of the _____ and the length of the segment on the hypotenuse _____ to the leg
leg,geometric, hypotenuse, adjacent
When given two sides of a right triangle you can find the _____ of the acute angles by using the ______ trig function
measures, inverse
The endpoints of a midsegment
midpoints
A _____ is created when two midpoints are joined
midsegment
A segment that has endpoints at the midpoints of two sides of a triangle will be _____ to the third side of the triangle and will be _____ its length
parallel, half
The lengths of two corresponding segments after a dilation with scale factor other than one or 0 are ____ to one another
proportional
The corresponding sides of similar figures are _____, but corresponding angles of similar figures at ______.
proportional, congruent
0 < K < 1
reduction
A dilation by the scale factor of 0.4 would result in a...
reduction
k=1/4
reduction
A dilation is described with a _____ and a ________.
scale factor & dilation
The _____ of the dilation controls the size of the image, while the _____ of dilation controls the location of the image.
scale factor, center
Theorem 2: altitude is not involved
side (leg) equal square root of whole hypotenuse times adjacent leg
Dilations create ____ figures
similar
The _____ ratio of a non-right angle of a right triangle is equal to opposite side divided by the ____ and its equivalent to the cosine ratio of the other actue angle in the right triangle
sine, hypotenuse
Parallelograms with corresponding angles are ____ similar
sometimes
side splitter theorem
states that if a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.
AAA
states that two triangles are similar if they have two corresponding angles congruent
Angle of Elevation
the angle between your line of sight the line connecting you straight to the object viewing upward
Vertices
the common endpoint of two or more rays or line segments
Hypotenuse
the longest sides of a right triangle
180(n-2)
the sum of the interior angles of any polygon
Dilation
transformation in which a figure grows or shrinks
A dilation is a type of _____ that creates ____ figures
transformation, similar
Proportion
two equivalent ratios
Geometric Mean
x equals square root of a times b
