Similarity Statements
similar figures have the same shape but are not necessarily ______________
the same size
What is the angle angle similarity theorem?
If two angles in one triangle are congruent to two angles in another triangle then the triangles are congruent.
What is the pythagorean theorem?
a^2+b^2=c^2
a ratio of the lengths of two sides in a right triangle
Trigonometric Ratio
5, 12, and 13 are a _________
Pythagorean Tripple
Figure PQRS is three times bigger than P''Q''R''S and Figure PQRS has all negative x points where P''Q''R''S has all positive x points. How is PQRS mapped onto P''Q''R''S?
A reflection in the y-axis followed by a dilation at a scale factor of 1/3
There are two right triangles. With two known angles. One has an acute angle of 26 degrees. The other has an acute angle of 64 degrees. Determine if these triangles are similar with a similarity statement
These triangles are similar by the AA similarity theorem because they add to 180
If the length of the two legs of a right triangle are 3 and 4 what is the length of the hypotenuse?
5
Opposite over adjacent
Tangent
what are the two types of special right triangles?
45-45-90 and 30-60-90
Similarity transformations preserve ___________
angle measures
If the corresponding side lengths of two triangles are__________ then they are similar
Proportional
if c^2 is less than a^2 + b^2 then the triangle is
acute
opposite over hypotenuse
Sine
the angle that an upward line of sight with a horizontal line
Angle of elevation
Side lengths in a triangle are changed in length due to a similarity transformation. But this, in relation to their side lengths, is not, which is also equal to the scale factor k
Ratios of corresponding side lengths
If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the ___________________ including this angle are proportional then the triangles are similar
Sides- side angle side similarity theorem
The value of c^2 is 400 and the value of a^2 plus b^2 is 313. What type of triangle is it?
Obtuse
in order to find the measure of an angle when you have the length of the adjacent and the length of the hypotenuse to the angle you should use
Inverse cosine
b^2=a^2+c^2-2bcCosA
Law of cosine
Triangle DEF is similar to triangle MNP. What is the value of EF if
ED is 15
NM is 18 and
NP is 30?
25
You have two right triangles and you know the lengths of their legs. How would you prove their similarity?
With the SAS similarity theorem
the sides of a triangle are 12, 16, and 20. What type of triangle is it?
right triangle
The measure of the hypotenuse of a triangle is 13. The measure of an acute angle is 25 degrees. What is the measure of the side opposite of this angle?
5.5
If you know two angles and a side you should use this theorem to solve a triangle
Law of Sines