Algebra
Solve for x: -x2-6x+16
x = -8, 2 or x = {-8, 2}
Triangle ABC ≅ triangle DEF. How can we prove AC ≅ DF?
CPCTC (Corresponding parts of congruent triangles are congruent)
When a transformation preserves the size and shape of the figure. All corresponding sides and angles are congruent between the image and the pre-image. (translation, reflection, rotation)
List all congruent angles and sides if △JKL ≅ △PQR.
∠J ≅ ∠P / ∠K ≅ ∠Q /∠L ≅ ∠R // JK ≅ PQ / KL ≅ QR / LJ ≅ RP
p: There are seven days in a week. q: March has exactly 30 days. Find the truth value of "p v q".
T
Factor using slip and slide: 3x2+7x=-2
x = (-1/3), -2 or x = {-2, -1/3}
Triangle ABC is isosceles. If ∠A ≅ ∠C, then AB ≅ CB.
Isosceles triangle theorem converse
A(3, 6), B(2, 5), C(4, 3), D(5, 5) // Translate: (x, y) -> (x-5, y-3). // Dilate (x, y) -> (3x, 3y)
A"(-6, 9), B"(-9, 6), C"(-3, 0), D"(0, 6)
Consider △JKL. Classify it by its sides: J(-7, -7), K(-9, -1), L(-1, -1).
Isosceles. (rad68, rad68, rad72)
If it is Sunday, there is no school. If there is no school, then I am happy. // If it is Sunday, then I am happy.
Law of Syllogism
Simplify: -5√8 + 2√45 + 3√200
-10√2 + 6√5 + 30√2
If ∠X is supplementary to ∠Y and ∠X is supplementary to ∠Z, then ∠Y ≅ ∠Z // If A||B and B||C, then A||C
Congruent supplements theorem // Transitive property of parallel lines
Triangle XYZ has vertices X(4, 7), Y(8, 5), Z(6, 3). Rotate the figure 90o about point P(1, 2).
X'(-4, 5), Y' (-2, 9), Z'(0, 7)
Which methods could be used to prove two triangles congruent given the following?: // Given: L is the midpoint of KN and MP.
SAS or SSS congruence theorem. (Midpoint gives us SS)
What is the equation for point-slope form?
y - y1 = m(x - x1)
Solve for x using the quadratic formula: 9x2-18x=7
x = (-1/3), (7/3) or x = {-1/3, 7/3}
Transversal c crosses line a and line b. If all angle measures of both line a and line b are congruent, name all five converses that prove lines to be parallel.
Corresponding ∠ converse // Alt. int. ∠ converse // Alt. ext. converse // consecutive int. ∠ converse // consecutive ext. ∠ converse
Parallelogram JKLM has vertices J(-1, 8), K(5, 6), L(7, -2), M(1, 0). Dilate by scale factor k = (1/2) about (-3, -2).
J'(-2, 3), K'(1, 2), L'(2, -2), M'(-1, -1)
If △DEF ≅ △JKL, DE=18, EF=23, DF=9x-23, JL=7x-11, and JK=3y-21, solve for X and Y.
X=6, Y=13
Consider △ABC where AB=4x+25, BC=3x-2, and AC=9x-5. What is the range for possible values for x?
4 < x < 14
Solve for x using completing the square: 2x2+4x=48
If ∠C is a right angle, then m∠C = 90o // If m∠P + m∠Q = 90o, then ∠P and ∠Q are complementary // If ∠M and ∠N form a right angle, then ∠M and ∠N are complementary.
Definition of a Right Angle // Definition of complementary angles // Complement Theorem
Identify the center of dilation and scale factor: X(5, 12), Y(14, -3), Z(-1, 0). X'(6, 8), Y'(12, -2), Z'(2, 0)
Center (8, 0), Scale factor 0.75
Consider △QRS: ∠Q = 90o, ∠R = 30o, ∠S = 60o. QR=8, RS=16, QS=8. Classify the triangle by its angles and sides. (Note: if invalid, write "N/A")
N/A
P(-2, 1)