SAT Math - Geo. + Trig. / Advanced Math

vertical angle

two angles directly across from each other in an intersection of two lines (they are equal)

supplementary angle

two angles on a straight line that are opposite to each other (add up to 180)

similar triangles (and what examples)

• have all the same angle measures

• thus have the same side length ratios

• a smaller triangle within a large triangle 

• triangles created by the intersection of two lines (only when cut off by two parallel lines on top and bottom 

What must you pay attention to when finding missing side lengths in a triangle?

• that you are matching up similar sides correctly 

• longest side of triangle A matches w longest side of triangle B, etc. 

How do you make the fractions in order to find a missing side length in similar triangles?

• larger triangle side goes on numerator

• matching smaller triangle side goes on denominator

• set it equal to another pair of matching sides from the two triangles

note: you do not place measures from the same triangle in a fraction

What is SohCahToa?

• sin = opposite/hypotenuse

• cos = adjacent/hypotenuse

• tan = opposite/adjacent

How do I find an angle of a right triangle, only given two side lengths? 

• Determine which angle you are given the opposite side of

• Set opp/hyp equal to sin(angle)

What angle are you looking for when asked for angle of MLN

angle of L

What is meant by shortest distance between two points?

hypotenuse

What is the measure for a right triangle when the two non-hypotenuse sides are equal?

45

How do you find arc length?

Set the ratio of the arc’s angle to the whole circle equal to the ratio of the arc length to the whole circle

eg. (135 degrees/ 360 degrees) = (arc length/circle circumference)

How do you convert from radian to degrees?

(radian measure/ pi) = (degree measure/ 180 degrees)

What is the circle equation? (eg. (x - 4)² + (y + 5)²  = 16) 

(x - h)² + (y - k)²  = r²

• r = radius

• (h, k) center 

eg.

• radius = 4

• center = (4, -5)

What is the equation of the circle doubled in size if the equation is (x - 4)² + (y + 5)²  = 16?

(x - 4)² + (y + 5)²  = 64

note: double the radius and then square it, not just what the equation is equal to

What does it mean when a line is tangent to a circle? 

one point on that line touches the outer edge of the circle

What is the altitude of a triangle?

a non-diagonal line line on a triangle

What must you look for if asked what point lies on a line that is tangent to a circle?

A point that lies on the slope of the line

Find slope by: using (y1 - y2) / (x1 - x2)

What should you pay attention to in problems involving overlapping triangles? 

• Make sure you see ALL existing triangles

• Outline them all to make sure you don’t miss any

What is the minimum/maximum value of a function?

the y-value of the vertex; UNLESS asked for the X of the minimum/maximum value

What do you enter an equation such as y = c as in DESMOS?

y = 0x + c

What does it mean when there are no solutions?

• lines never intersect

• lines are parallel 

• lines have the same slope

Should you use DESMOS for a problem involving no solutions to a quadratic?

Yes

Should you use DESMOS for a problem involving no solutions to a system of two lines/linear functions?

No; use paper and pencil

What should I NOT use DESMOS for?

Algebra