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