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Kites: A kite is a quadrilateral with the following properties: Exactly two consecutive congruent sides (eq. AB=AD and BC=DC) and one pair of opposite angles are congruent (eq. <ABC=<ADC)

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Midsegment of a trapezoid: The midsegment of a trapezoid connects the midpoints of the legs. (eq. AB||CD||EF)

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Non-Isosceles Trapezoids: Only one pair of opposite sides are parallel and Consecutive angles between parallel lines are supplementary. (eq. <C=149=180-31)

Isosceles Trapezoids: Non-parallel sides are congruent, Diagonals are congruent, base angles are congruent, opposite angles are supplementary. (eq. DG=EF)

Image Credits: Enrique Sierra

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Squares: They have all the properties of a parallelogram, a rectangle, and a rhombus. (eq. BC=AD)

Image Credits: Enrique Sierra

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Rhombi: All properties of parallelograms and 4 sides are congruent, diagonals are perpendicular, and diagonals bisect opposite angles. (eq. JK=12=JM)

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Rectangles: Follow all the rules of Parallelograms, including these: All four corners are right angles, and the diagonals are congruent. (eq. <ABC=90 degrees)

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Parallelograms: A quadrilateral in which both pairs of opposite sides are parallel. Their opposite angles and sides are congruent, their consecutive angles are supplementary, and diagonals bisect each other. (eq. AB=15 CD=15)

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 Triangle Congruence: SSS, SAS, ASA, AAS, HL

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 Triangle Congruence: SSS, SAS, ASA, AAS, HL

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SSS (Side-Side-Side)Triangle: Three pairs of congruent sides. (eq. △ABC=△DEF = SSS)

SAS (Side-Angle-Side) Triangle: Two sides and an included angle are congruent (eq. △ABC=△DEF = SAS)

ASA (Angle-Side-Angle) Triangle: Two angles and an included side are congruent (eq. △ABC=△DEF = ASA)

AAS (Angle-Angle-Side) Triangle: Two angles and a side opposite them are congruent (eq. △ABC=△DEF = AAS)

HL (Hypotenuse Leg) Triangle: The hypotenuse and any one leg of a right triangle are congruent. (eq. △ABC=△DEF = HL)

Image Credits: Enrique Sierra

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Point slope: y-y1=m(x-x1)

(eq. (y-1=2[x-4]) = (y=2x-7))

Standard Form: Ax+By=C

(eq. (x+y=6) = (y=-x+6))

Image credits: Enrique Sierra

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Parallel Lines: Two coplanar lines that never intercept. "||" is the symbol that represents parallel lines (eq. Line AB || Line CD).

Perpendicular Lines: Lines that intersect at a right angle. The symbol is "⊥" (eq. Line L ⊥ Line M).

Image Credits: Enrique Sierra

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Conditional Statements and Venn Diagrams

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Conditional Statements and Venn Diagrams

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Conditional Statement: A statement that can be written in "if...,then" form (p->q). Hypothesis follows "if" and conclusion follows "then." (eq. "If an angle has a measure greater than 90 degrees, then it's an obtuse angle.")

Venn Diagrams: Useful way to show relationships. All elements of p are elements of q (eq. Every natural number is a whole number), some elements of p are elements of q (eq. Some vertical angles are complementary), there is no relationship between p and q (eq. irrational numbers are never rational numbers).

Image credits: Enrique Sierra

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Point: a location with no length or width; written with a capital letter. (eq. Point P)

Line: an infinite amount of points. It has no length or height. (eq. Line PQ)

Plane: a flat surface made up of points. 3 points are needed. It extends indefinitely in all directions. (eq. Plane PQR)

Distance Formula: d=√(x2-x1)^2+(y2-y1)^2

(eq. d=√(-5--2)^2+(3--3)^2)

Midpoint Formula: (x1+x2/2, y1+y2/2)

(eq. [7+9/2,-5+-1/2])

Image credits: Enrique Sierra