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GEOMETRY SOL IDEAS

GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each other. They are equal. Constructions (Use tracing paper! ) paper ruler, plastic compass 1. Segment / Angle Bisector

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GEOMETRY SOL IDEAS

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  1. GEOMETRY SOL IDEAS

  2. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each other. They are equal.

  3. Constructions (Use tracing paper!) paper ruler, plastic compass 1. Segment / Angle Bisector 2. Congruent Segments / Angles 3. Perpendicular lines (90 degrees) 4. Perpendicular bisector

  4. ISOSCELES EQUI Venn Diagrams intersection = common no intersection  nothing in common Circle inside another circle “All bulldogs are dogs.”

  5. Conditional (p  q) Converse (q  p) switch Inverse (p q) not-not Contrapositive (q p) Symbolic Representation p: the opposite of p

  6. Parallel Lines (only 2 Options: = or 180) alternate interior angles ( = ) Zorro alternate exterior angles ( = ) corresponding angles ( = ) consecutive interior angles (180)

  7. Parallel lines have EQUAL slopes. Perpendicular lines have ‘opposite reciprocal’ slopes. 2/3 & -3/2 Compute SLOPES visually. from left to right, count rise over run.

  8. Triangle Sum Theorem The sum of the 3 angles is 180. An equilateral triangle is always a 60-60-60 triangle. An equilateral triangle is isosceles. (3 = sides means 2 = sides)

  9. The base angles of an isosceles triangle are congruent. (BAT) Ext. Angle Theorem: out = in + in SAS, SSS, ASA, AAS (no SSA) Use ticks & arcs.

  10. Triangle Inequality Ideas The bigger the angle, the longer the opposite side, & vice-versa. Draw and label a figure! S, M, L or L, M, S Arrange from least to greatest, greatest to least… (be careful!)

  11. Triangle Inequality Theorem sum of 2 shorter sides >3rd side Technique: Add 2 sides, Subtract 2 sides (This gives the possible values for 3rd side.)

  12. Similar triangles: corresponding sides are proportional (EQ:ratio = ratio) S/S = M/M = L/L Corresponding angles are congruent. The sequence of letters is important!

  13. Proportionality Theorems part / part = part / part (for any two SIMILAR figures) ratio of perimeters = scale factor (ratio of sides)

  14. Pythagorean Theorem Pythagorean Triples (5,12,13 ; 7, 24, 25 ; 3, 4, 5 ; etc.) The altitude drawn to the hypotenuse gives rise to THREE similar triangles. (tic-tac-toe)

  15. Special Right Triangles (shortcuts) • 45-45-90 (half-square) • legs are = • a  c: multiply bysq. rt. of 2 • 30-60-90 • a  c: multiply by 2 • a  b: multiply by sq. rt. of 3

  16. Trigonometry [Degree Mode!!] 3 steps: Label the sides. (eyeball) EQ: SOH-CAH-TOA Cross-multiply elevation = depression Zorro

  17. COODies for Parallelograms (Set up equation based on these properties.) Special Properties Diagonals of a rhombus are perpendicular. Diagonals of a rectangle are =.

  18. Transformations or Movements (translation, rotation, reflection) ‘slide’ ‘turn’ ‘flip’ Symmetry Lines for Polygons regular polygons  ‘n’ sides Point Symmetry (hexagon, S, O, N) (when you turn by 180, you get same picture)

  19. Rotation: Center & Angle (connect technique) Reflection: Across Different Axes Translation: sliding an object Images of Points (X, Y, Z  X’, Y’, Z’) Watch out for the correspondence!

  20. Tangents & Ice Cream Cones Tangent line is perpendicular to the radius. Use P.T. Angle-Arc Relationships 1. Central Angle = Opposite Arc 2. Inscribed Angle is ½ of Arc

  21. 180 and 360degree principles Semi-circle = 180 (diameter) Inscribed angle that cuts a semi-circle = 90 (L-shape)

  22. Segment relationships (part)(part) = (part)(part) (out)(total) = (out)(total) tangent squared = (out)(total) Other angle-arc relationships in: (BIG + SMALL) / 2 (x – 2)^2 + (y + 5)^2 = 16 Center: (2, -5) and radius r = 4

  23. Polygon Formulas (MEMORIZE) (n – 2)(180)  sum of interior angles Divide the above by n  measure of EACH interior angle (regular polygons) n  number of sides (also the number of angles)

  24. 360  sum of exterior angles 360 / n  each exterior angle 360 / ext. angle  n (sides) The exterior & interior angles of any polygon add up to 180. (‘extend a side’ technique)

  25. Areas of Similar Polygons (ratio of sides) squared Circumference and Arc Length divide angle by 360 first Areas of Sectors (pizza slice) divide angle by 360 first Then multiply…

  26. 3 dimensional figures (scaling, fitting in a piece, nets) 3 perspective views (top, side, front)  use common sense!

  27. Surface Area and Volume Formulas (5 solids) Use Formula Sheet! B  area of base (8 x 8) h  height l  slant height (use P.T.) r  radius (half of diameter)

  28. Similar Figures / Solids Ratio of Sides = Scale Factor Ratio of Areas (squared/squared) if scale is 2:3, then areas ratio is 4:9 Ratio of Volumes (cubed/cubed) if scale is 2:3, then volumes ratio is 8:27 Some problems don’t require the use of formula sheet. Set up ratio = ratio.

  29. Label points first! (x1,y1) & (x2,y2) Use techniques shown in class. Slope: Distance: Midpoint: add & divide by 2

  30. Good Luck! Give it your best shot! (time incentive)

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