Module 1:
Reasoning with Shapes
Reasoning with Shapes
180 degrees
What is the sum of the Interior Angles of a triangle?
What is the measure of a Straight Angle/line?
What is the sum of supplementary angles?
Prove SSS, SAS, or ASA
How do you determine the congruence of two triangles?
This segment splits an angle in half.
What is an Angle Bisector?
y = 2x + 3
y = 2x - 5
1/2 or 50% chance
What is the probability of landing on heads when flipping a coin?
What is the probability of landing on tails when flipping a coin?
Lines that never intersect and remain equidistant forever
What are Parallel Lines?
A pair of angles that are on opposite sides of the transversal on the outside of the parallel lines.
What are Alternate Interior Angles?
We use cross multiplication (or the butterfly) when we solve for this.
How do you find the length of a segment in similar triangles?
Given: y = mx + b
The slope.
What does m represent in y = mx + b?
Used to determine the number of outcomes in a sample space
The Counting Principle
m*n*...
30-60-90 or 45-45-90
What are the angle measures in Special Right Triangles?
A shape with two pairs of opposite parallel sides.
What is a parallelogram?
We use this when dilating figures or finding area/perimeter of similar figures?
What is the Scale Factor?
Preimage:
A(1, 2), B(3, 2), C(1, 5), D(3, 5)
Image:
A'(5, 10), B'(15, 10), C'(5, 25), D'(15, 25)
What is a dilation of the preimage ABCD with scale factor of 5 to create the image A'B'C'D'?
Independent Events
What are the type of events where the occurrence of one event have no impact on the occurrence of the other?
This measurement of a shape is exactly half of the distance across the shape (through it's center).
What is the relationship between the radius and diameter of the circle?
AA, HL, HA
What are triangle congruence theorems specific to right triangles?
The side length ratio opposite/hypotenuse.
What is the sine ratio?
A transformation that maps a shape onto itself.
What is a rotation of 360 degrees?
What is reflection over a line of symmetry?
What is a sequence of translations the same distance up as down or left as right?
Probability Model
How can we display the outcomes and probability of them occurring?
This measure in a circle is equal to the measure of the corresponding arc in that circle.
What is the central angle measure in a circle?
A line or segment that splits a segment in half and creates a 90-degree angle.
What is a Perpendicular Bisector?
SOHCAHTOA
What is the acronym to remember trigonometric ratios?
What is sine(A)=opp/hyp; cosine(A)=adj/hyp; tangent(A)=opp/agj?
(x - h)2 + (y - k)2 = r2
What is the equation of a circle?
P(A)*P(B) vs.
P(A) + P(B) - P(A and B)
What is the difference in the equations to solve for P(A and B) versus P(A or B)?