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 2. Congruent Segments / Angles3. Perpendicular lines (90 degrees)4. Perpendicular bisector

Venn Diagrams

intersection = commonno intersection nothing in commonCircle inside another circle “All bulldogs are dogs.”

ISOSCELES

EQUI

Conditional (p q)Converse (q p) switch Inverse (p q) not-notContrapositive (q p)

Symbolic Representation p: the opposite of p

Parallel Lines

(only 2 Options: = or 180)

alternate interior angles ( = ) Zorroalternate exterior angles ( = )corresponding angles ( = ) consecutive interior angles (180)

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.

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)

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.

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!)

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.)

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!

Proportionality Theorems part / part = part / part

(for any two SIMILAR figures)ratio of perimeters = scale factor (ratio of sides)

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)

Special Right Triangles (shortcuts)

1. 45-45-90 (half-square) legs are = a c: multiply by sq. rt. of 2

2. 30-60-90 a c: multiply by 2 a b: multiply by sq. rt. of 3

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

elevation = depressionZorro

COODies for Parallelograms (Set up equation based on these properties.)

Special Properties Diagonals of a rhombus are perpendicular. Diagonals of a rectangle are =.

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)

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!

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

180 and 360 degree principles

Semi-circle = 180 (diameter)

Inscribed angle that cuts a semi-circle = 90 (L-shape)

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 = 16Center: (2, -5) and radius r = 4

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)

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)

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…

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

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)

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.

Label points first! (x1,y1) & (x2,y2)Use techniques shown in class.

Slope:

Distance:

Midpoint: add & divide by 2

Good Luck! Give it your best shot!

(time incentive)