Download Important things to remember for the Geometry EOC

Important things to remember for the Geometry EOC:
1. Conditionals: “If (hypothesis) , then (conclusion)”
a. Converse: “FLIP”
b. Inverse: “SAY NO”
c. Contrapositive: “FLIP AND SAY NO”
d. COUNTEREXAMPLE: Example that proves something is FALSE.
2. Biconditionals: “… , if and only if …”
a. ONLY IF CONDITIONAL AND CONVERSE ARE BOTH TRUE!
3. Translations: “SLIDE”
a. (x,y)  (x
– h, y – k)
LEFT
RIGHT
UP
DOWN
4. Rotations: “TURN”
a. Assume COUNTERCLOCKWISE
5. Reflections: “FLIP”
a. Over x-axis – opposite y-coordinate
b. Over y-axis – opposite x-coordinate
c. Over y = x – swap x and y coordinate
6. Glide Reflection: “Slide then Flip”
7. Dilations:
a. Enlargement: scale factor > 1
b. Reduction: 0 < scale factor < 1
8. Symmetry:
a. Line symmetry (or reflectional symmetry)
b. Rotational symmetry (angle of rotation where figure repeats)
c. Point symmetry (figure repeats every 180º)
9. Tessellations: Repeated tile pattern, no gaps or overlaps
10.Angles Pairs
a. Complementary (add up to 90)
b. Supplementary (add up to 180)
c. Vertical (are congruent)
d. Linear pair (are supplementary)
11.Constructions
12.Triangles
a. By sides: Equilateral (all sides , all s 60º), Isosceles (base s ), Scalene
b. By Angles: Acute, Obtuse, Right, Equiangular
c. Midsegment: connects midpoints of 2 sides; & it’s HALF of the side that it is
parallel to.
13.Proofs
a. Theorems
b. Definitions
c. Postulates
d. Properties (of equality, etc)
14. Undefined Terms
a. Points
b. Lines
c. Planes
15.Points of Concurrency in Triangles:
a. CIRCUMCENTER: Perpendicular Bisectors
i. Equidistant to the vertices
b. INCENTER: Angle Bisectors
i. Equidistant to the sides
c. CENTROID: Medians
i. Median: segment from vertex to midpoint of opposite side
ii. Shorter length of median is half the longer length of median
d. ORTHOCENTER: Altitudes
i. Altitude: segment from vertex that is perpendicular to opposite side
16.Proving Triangles Congruent:
a. SSS, SAS, ASA, AAS, HL (HL only proves RIGHT TRIANGLES )
b. Use CPCTC to prove “Corresponding Parts of Congruent Triangles and
Congruent”. *Use CPCTC AFTER proving triangles congruent!
17.Proving Triangles Similar:
a. SSS~, SAS~, AA~
b. Use proportions to find: scale factor & missing sides
18.Triangle Inequalities:
a. Opposite of the LARGEST ANGLE is the LONGEST SIDE.
b. Sum of 2 sides is ALWAYS greater than the third.
c. If a2 + b2 > c2, then the triangle is ACUTE.
d. If a2 + b2 < c2, then the triangle is OBTUSE.
19. GEOMETRIC MEAN of a and b: √𝑎𝑏
20.Parallel Lines/ Transversals
a. See picture… 
b. ALTERNATE INTERIOR ANGLES (4 & 6, 3& 5), ALTERNATE
EXTERIOR ANGLES (1 & 7, 2 & 8), and CORRESPONDING ANGLES(1 &
5, 2 & 6, 3 & 7, 4 & 8) ARE CONGRUENT!!!
c. SAME-SIDE INTERIOR ANGLES ARE SUPPLEMENTARY!!!
21. Right triangles
a. Right Triangle similarities
i. a2 = b(b+c)
ii. d2 = c(b+c)
iii. e2 = bc
b. Pythagorean Theorem (a2 + b2 = c2)
i. Pythagorean Triples: (3,4,5),(5,12,13),(9,40,41),(7,24,25),(8,15,17)
c. Special Right Triangles
i. 30-60-90--- x-x√3-2x
ii. 45-45-90--- x-x-x√2
d. SOH-CAH-TOA
i. Angle of Elevation
ii. Angle of Depression (from the horizontal, downward)
22.DISTANCE FORMULA/ MIDPOINT FORMULA
a. Distance = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
𝑥1 +𝑥2 𝑦1 +𝑦2
b. Midpoint: (
2
,
2
)
c. “AB” without the segment symbol means “length of segment AB”.
23.Polygons
a. Angle-Sum Theorem (S= (n – 2)180)
b. Sum of Exterior Angles= 360 *No matter how many sides!
c. Midsegment of triangle (half the length of parallel side)
24. Quadrilaterals
a. Properties of Parallelograms, Rhombuses, Squares, Rectangles, Kites, Trapezoids
b. Midsegment of Trapezoids (Midsegment is average of the bases)
25. Circles
a. Equation of a Circle: (x – h)2 + (y – k)2 = r2
i. Center: (h,k)
ii. Radius: r
̂
𝑚𝐴𝐵
b. Circumference (2πr) & Arc Length (
̂
𝑚𝐴𝐵
c. Area (πr2) and Sectors (
360
360
∙ 2𝜋𝑟)
∙ 𝜋𝑟 2 )
d. Segments of Circles (Area of “slice” MINUS area of triangle)
e. Arcs
f. Tangent lines (perpendicular to a radius)
g. Angle Measures and Segment Lengths
26. Area- ALWAYS IN SQUARED UNITS!
a. Parallelograms, Triangles, Kites, Trapezoids, Rhombuses, squares, rectangles,
regular polygons (KITE FORMULA IS NOT ON FORMULA SHEET!)
27.Solids (Prisms, Cylinders, Pyramids, Cones, Spheres)
a. EULER’s FORMULA
i. 2-dimensional: F + V = E + 1
ii. 3-dimensional: F + V = E + 2
b. Cross sections
c. Surface Area (and/or Lateral Area)- ALWAYS IN SQUARED UNITS!
d. Volume- ALWAYS IN CUBIC UNITS!
28.Similar Figures
a. SCALE FACTOR: a/b
b. RATIO OF PERIMETERS: a/b
c. RATIO OF AREAS: a2/b2
d. RATIO OF VOLUMES: a3/b3