geometry U3-4 Flashcards
Properties of dilatons
Angles remain the same
Sides are proportional
Corresponding line segments on the preimage and image are parallel
the center MUST be collinear with all the corresponding points and points on the image/preimage
The center can’t be in between the preimage and image
Theorems of proving triangles similar (IMPORTANT)
AA
SSS
SAS
HL (for right triangles)
(If the sets of corresponding sides are similar)
Scale factor of Area & Volume
To find the volume of a shape’s image:
Take the preimage and multiply the volume to the scale factor cubed
To find the area of a shape’s image:
Take the preimage and multiply the area to the scale factor squared
Within & Between ratios
Within (within a fraction)
Between (Between 2 fractions)
Notation for dilation
D (C, K)
D is dilation
C is the center
K is the Scale factor
What is true about the order of the letters?
They have to maintain the same order in both.
What is an altitude? What is true about it?
It is a line segment from a vertex to an opposite side of a triangle. it splits the triangle into 2 similar triangles, and those 2 similar triangles are similar to the original triangle.
Formula for an altitude (height) of a triangle (is also geometric mean) (STAR) DRAW THIS OUT
Square root of (A*B)
Leg rule (STAR) DRAW THIS OUT
This is used to find missing sides.
You have to first mentally shrink/expand one triangle and rotate it so you can see they’re similar.
you have to set up a cross-multiplication proportion involving the corresponding sides that map on top of each other.
NOTE: YOU MUST SIMPLIFY FRACTIONS AS YOU NORMALLY WOULD.
How to:
Add radicals
Subtract radicals
Multiply radicals
Divide radicals
Rationalize a denominator
GO ONLINE AND FIND SOME PROBLEMS TO SOLVE ON THE SPOT AND EXPLAIN AS YOU ARE SOLVING THEM.
NOTE: YOU MUST SIMPLIFY FRACTIONS AS YOU NORMALLY WOULD.
NOTE: YOU MUST SIMPLIFY FRACTIONS AS YOU NORMALLY WOULD.
TO ADD: You need like terms under the hat. Simplify what’s under the hat and multiply what you get out to what’s outside the hat. Add as usual and then simplify.
TO SUBTRACT: Same thing as adding, but with subtraction.
TO MULTIPLY: You can multiply what’s inside and outside the 2 radicals with no problem, even if they’re not like terms. You have to simpolify after, though.
TO DIVIDE: You can either simplify what’s under the hat and divide like that, or you can directly divide what’s under the hat and then simplify.
TO RATIONALIZE: You need to multiply the whole fraction by what’s in the denominator, simplify from there.
NOTE: YOU MUST SIMPLIFY FRACTIONS AS YOU NORMALLY WOULD.
NOTE: YOU MUST SIMPLIFY FRACTIONS AS YOU NORMALLY WOULD.
NOTE: YOU MUST SIMPLIFY FRACTIONS AS YOU NORMALLY WOULD.
Special right triangles (DRAW THIS OUT)
Either a pythagorean triple (test triangle first to see if it is one),
A special right triangle:
With the angles 45, 45, 90 (the ratio is x:x:x*the square root of 2)
*Or, with the angles 30, 60, 90 (the ratio is: Hyp. is 2x, Side between 30 and 90 degrees is Xsquarerootof3, and sidebetween60and90is X.
You can remember this by:
Hypotenuuuse, 2x
Side between bigger numbrs (between 60 and 90) has less characters (just X), and
Side between smaller numbers (30 and 90) has more characters (x times square root of 3).
Methods of solving for unknown side lengths
DO THESE IN ORDER EVERY TIME YOU SEE A TRIANGLE:
Pythagorean theorem,
special right triangle, and
trigonometry
Explain what a cofunction and inverse ratio is.
You know what this is, just explain it.
Angle of elevation/depression (DRAW THESE OUT)
Angle of elevation is an angle that starts where the viewer is looking from and goes to the object
Angle of depression is made up a horizon where the object is and then the downward angle.
