![Page 1: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/1.jpg)
GEOMETRY SOL IDEAS
![Page 2: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/2.jpg)
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.
![Page 3: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/3.jpg)
Constructions (Use tracing paper!) paper ruler, plastic compass
1. Segment / Angle Bisector 2. Congruent Segments / Angles3. Perpendicular lines (90 degrees)4. Perpendicular bisector
![Page 4: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/4.jpg)
Venn Diagrams
intersection = commonno intersection nothing in commonCircle inside another circle “All bulldogs are dogs.”
ISOSCELES
EQUI
![Page 5: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/5.jpg)
Conditional (p q)Converse (q p) switch Inverse (p q) not-notContrapositive (q p)
Symbolic Representation p: the opposite of p
![Page 6: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/6.jpg)
Parallel Lines
(only 2 Options: = or 180)
alternate interior angles ( = ) Zorroalternate exterior angles ( = )corresponding angles ( = ) consecutive interior angles (180)
![Page 7: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/7.jpg)
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.
![Page 8: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/8.jpg)
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)
![Page 9: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/9.jpg)
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.
![Page 10: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/10.jpg)
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!)
![Page 11: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/11.jpg)
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.)
![Page 12: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/12.jpg)
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!
![Page 13: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/13.jpg)
Proportionality Theorems part / part = part / part
(for any two SIMILAR figures)ratio of perimeters = scale factor (ratio of sides)
![Page 14: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/14.jpg)
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)
![Page 15: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/15.jpg)
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
![Page 16: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/16.jpg)
Trigonometry [Degree Mode!!]3 steps: Label the sides. (eyeball) EQ: SOH-CAH-TOA Cross-multiply
elevation = depressionZorro
![Page 17: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/17.jpg)
COODies for Parallelograms (Set up equation based on these properties.)
Special Properties Diagonals of a rhombus are perpendicular. Diagonals of a rectangle are =.
![Page 18: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/18.jpg)
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)
![Page 19: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/19.jpg)
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!
![Page 20: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/20.jpg)
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
![Page 21: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/21.jpg)
180 and 360 degree principles
Semi-circle = 180 (diameter)
Inscribed angle that cuts a semi-circle = 90 (L-shape)
![Page 22: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/22.jpg)
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
![Page 23: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/23.jpg)
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)
![Page 24: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/24.jpg)
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)
![Page 25: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/25.jpg)
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…
![Page 26: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/26.jpg)
3 dimensional figures (scaling, fitting in a piece, nets) 3 perspective views (top, side, front) use common sense!
![Page 27: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/27.jpg)
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)
![Page 28: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/28.jpg)
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.
![Page 29: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/29.jpg)
Label points first! (x1,y1) & (x2,y2)Use techniques shown in class.
Slope:
Distance:
Midpoint: add & divide by 2
![Page 30: GEOMETRY SOL IDEAS. Complementary angles have the sum of 90. Angles that form a LINEar pair are supplementary (180). Vertical angles are opposite each](https://reader036.vdocuments.site/reader036/viewer/2022062407/56649e395503460f94b2b4e1/html5/thumbnails/30.jpg)
Good Luck! Give it your best shot!
(time incentive)