Units 1 and 2
What is the distance formula?
√Δx2+Δy2
What are skew lines?
Noncoplanar lines that never intersect
What 5 theorems prove that triangles are congruent?
SSS≅Thm
SAS≅Thm
ASA≅Thm
AAS≅Thm
HL≅Thm
Find AB
A(2, 5)
B(-6, -1)
AB=10 units
ΔABC has vertices A(-2,4), B(3,5), and C(5,4)
Find the coordinates of the vertices of ΔA'B'C' after a reflection in the y-axis
A'(2,4), B'(-3,5), and C'(-5,4)
Which x and y values does QI represent in the coordinate plane?
(+x, +y)
What is a line that cuts through two parallel lines called?
Transversal
Why isn't AAA a theorem?
Triangles can have the same angle measures, but also not have the same side lengths
Use Distributive Property
2(3x+5)=46
x=6
ΔABC has vertices A(-2,4), B(3,5), and C(5,4)
Find the coordinates of the vertices of ΔA'B'C' after a 90° rotation about (0,0)
A'(-4,-2), B'(-5,3), and C'(-4,5)
What property says that a(b+c)=ab+ac?
Distributive Property
What types of angles give you congruent angles in a parallel-transversal situation?
Alternate Interior, Alternate Exterior, and Corresponding Angles
Why isn't SSA a theorem? (excluding right triangles)
The angle has to be in between the two sides
3(2x+6)=30
1.6x+18=30(Distributive Property)
2.6x=12(Subtraction)
3.x=2(Division)
If ΔABC≅ΔDEF, List each pair of congruent parts
AB≅DE
BC≅EF
CA≅FD
<ABC≅<DEF
<CAB≅<FDE
<BCA≅<EFD
What postulate says that adjacent angles that form a line are supplementary?
Linear Pair Postulate
What is a glide reflection?
A translation followed by a reflection
What is the Polygon Sum Theorem?
The sum of the interior angles of any polygon is equal to 180 times 2 less than the total number of sides.
Ray BD is in <ABC. If m<ABD=20° and m<ABC=70°, what is m<CBD?
m<CBD=50°
In Quadrilateral ABCD, AB≅CD and AB||CD
Is ABCD a parallelogram? Why?
ABCD is a parallelogram because it has a pair of sides that are both parallel and congruent. (SC for ▱ #5)
When writing a two-column proof, what information should you write down as your first step?
Whatever information is needed first
What is a rigid motion?
A transformation resulting in congruence
List the properties of Parallelograms
1. Parallelograms have opposite sides parallel
2. Parallelograms have opposite sides congruent
3. Parallelograms have opposite angles congruent
4. Parallelograms have consecutive angles supplementary
5. Parallelograms have diagonals that bisect each other
A---------->-------E--------B
|
C---------->------F----------D
If m<AEF=100°, what is m<EFC?
m<EFC=80°
In quadrilateral ABCD, AB||CD and BC≅AD. What is ABCD? What isn't ABCD?
ABCD is an isosceles trapezoid because it has only 1 set of parallel sides and its non-parallel sides are congruent.
ABCD is not a parallelogram because it has only 1 set of parallel sides.
ABCD is also not a kite because opposite sides are congruent.