# Modified and Animated By Chris Headlee Apr 2014 Modified and Animated By Chris Headlee Apr 2014 SSM: Super Second-grader Methods Ch 2 Coordinate Relations and Transformations SSM: match up like variables If then is symbolically , and two angles are congruent is q, and angles are

vertical angles is p Coordinate Relations and Transformations Ch C SSM: measure ST to find midpoint use ruler to line up perpendicular Use compass to measure the same length arc from point S above and below. do the same from point T. Connect the intersections.

Coordinate Relations and Transformations Ch 3 SSM: look for angles the same Supplementary angles are usually one acute and one obtuse. A pair of congruent angles is not usually supplementary Coordinate Relations and Transformations

Ch C SSM: big arc centered at D eliminate answers that dont make sense Constructions marks are a bisection of angle D Coordinate Relations and Transformations Ch 2

SSM: test each area * Flute and oboe is the intersections of the Flute and Oboe circles. Overlaps with other circles must be eliminated because of the word only Ch C Coordinate Relations and Transformations SSM:

use ruler to measure mouth Draw an arc centered at A. Draw same length arc centered at B. Measure the distance from intersection on the lower ray to the upper ray with A Create same length arc on B from intersection on lower arc Coordinate Relations and Transformations Ch 3

SSM: Must use a and b and only one transversal Option B shows consecutive exterior angles which are supplementary Option D shows corresponding angles between c and d. Ch 2 Coordinate Relations and Transformations SSM: look for conclusion that has the

parts of the statements draw figures to illustrate answers Rhombus is parallelogram and parallelogram has opposite angles congruent; so combine rhombus has opposite angles congruent Ch 3 Coordinate Relations and Transformations SSM: x is a medium to large acute angle

Corresponding angles of parallel lines are congruent Coordinate Relations and Transformations Ch 1 SSM: draw figure draw lines of symmetry Distance formula or Pythagorean theorem Rise = 17 and run = 8

172 + 82 = d2 289 + 64 = 353 = d2 353 = d Coordinate Relations and Transformations Ch 3 SSM: plot points use slope definition Parallel lines have the same slope. Use points given to figure out the slope of line t

(rise = -8 and run = 16), which is -1/2. Use that slope and rise/run to draw a line through point P and plot a point along that line. Ch C Coordinate Relations and Transformations SSM: eliminate answers that do not fit Point p is not on the line and the line through it is perpendicular. No line segments are present

Coordinate Relations and Transformations Ch 2 SSM: inverse negate Remember the order: converse flip inverse negate

contrapositive both Negate the hypotheses and the conclusion. Coordinate Relations and Transformations Ch 9 V is (3, -8) and a reflection over the line y = x has (x, y) (y, x) So V is (-8, 3) SSM:

draw line equal distance Coordinate Relations and Transformations Ch 3 SSM: by eyes: angles equal 43 3x + 14 = 143 (alternate exterior angles) 3x = 129

x = 43 Ch 3 Coordinate Relations and Transformations SSM: draw points on graph find slope 73 4 slope = m = ------------- = ------------- = 1/2

5 (-3) 8 Coordinate Relations and Transformations Ch 9 SSM: draw lines of symmetry on graphs Draw the two lines (x = is a vertical line, y = is a horizontal line)

Coordinate Relations and Transformations Ch 3 SSM: Angle CBA is a large obtuse angle Angle CBA = angle ABH + angle HBC = 90 + supplementary with 115 (consecutive interior) = 90 + 65

= 155 Coordinate Relations and Transformations Ch 8 SSM: x is opposite larger angle eliminate A and B X is the adjacent side of the 20 angle. Use trig: cos 22 = x/80

80 cos 20 = x 75.17 = x Ch 4 Quadrilateral ABCD would be a rhombus with all sides equal. Diagonals divide a rhombus into 4 congruent triangles. Coordinate Relations and Transformations SSM:

draw figures on graph paper and compare Coordinate Relations and Transformations Ch 5 SSM: any two sides bigger than third 19 67

Use the following formula to find the bounds of the third side: Lg sm < third side < Lg + sm 43 24 < third side < 43 +24 19 < third side < 67 Coordinate Relations and Transformations Ch 8 SSM: right triangle Pythagorean theorem (on formula sheet)

Have to use each set of numbers in the Pythagorean theorem to see which works 202 + 212 = 292 400 + 441 = 841 841 = 841 Ch 4 Coordinate Relations and Transformations SSM: use eyes to see which are the same

Side opposite 45 degree angle must be 10 and all three angles must be the same. Triangle Rs angles are not the same as Q and S. Ch 5 Coordinate Relations and Transformations SSM: draw triangle Draw a triangle and label the sides and angles with what is given Find the missing angle (180 (45 + 68) = 180 113 = 67)

Put angles in order from least to greatest: 45 < 67 < 68 Put in the missing sides from angle descriptions: clarinet < flute < trumpet Ch 8 Coordinate Relations and Transformations SSM: height is smaller than 14 eliminate A and B Special case right triangles; side opposite 60 = hypotenuse 3

hypotenuse = 14, so answer is (14) 3 = 7 3 Ch 7 Coordinate Relations and Transformations SSM: isosceles Eliminate C Isosceles triangle with legs bigger than the base. Only triangles A and B satisfy that. Scaling factor of only fits triangle A completely.

Coordinate Relations and Transformations Ch 4 SSM: label angles and sides Reflexive Property Side-Side-Side (SSS) Theorem Reflexive is the something = itself

3 Sides are only mentioned. Coordinate Relations and Transformations Ch 8 SSM: hypotenuse is largest side length > 20 Eliminate A and B 20 foot side is opposite of the 38 angle, so we can us sine sin 38 = 20 / hyp

hyp sin 38 = 20 hyp = 20 / sin 38 hyp = 32.49 Coordinate Relations and Transformations Ch 7 SSM: draw figure draw lines of symmetry Similar triangle proofs (AA, SAS and SSS) CBD and ABE have right angles and a 2:1 ratio between long and short legs

of the right triangle Ch 4 Coordinate Relations and Transformations SSM: Angle and Side marked Eliminate A and C (no right angle) Angle and Side marked. Hidden feature is vertical angles. Since side is not between the two angles, AAS fits. Ch 5

Coordinate Relations and Transformations SSM: any two sides greater than third Add two shortest and compare with longest, if greater then triangle 6 + 8 = 14 not > 14 no triangle 9 + 11 = 20 not > 21 no triangle 8.5 + 10.5 = 19 > 17 triangle

4.7 + 4.7 = 9.4 not > 14 no triangle Ch 7 Coordinate Relations and Transformations SSM: order rules shared angle R Similarity theorems (AA, SAS, SSS) with shared angle R, either another corresponding angle or the sides on both sides of angle R.

Options A and B do not fit order rules. Option D has the correct sides. Coordinate Relations and Transformations Ch 6 SSM: rhombus: sides equal 9 Rhombus: all sides equal 6x 5 = 4x + 13 6x = 4x + 18 2x = 18

x=9 Coordinate Relations and Transformations Ch 6 SSM: large obtuse angle no real help Once around a point is 360. Interior angle of equilateral triangle is 60 and the interior angle of a nonagon is 140 (180 Ext angle: ext angle = 360/9). Angle JKL = 360 (140 + 60) = 360 200 = 160

Ch 10 Coordinate Relations and Transformations SSM: find equation on equation sheet Use equation from the equation sheet and substitute the center into equation. Remember that the negative of a negative is a positive. Coordinate Relations and Transformations

Ch 12 SSM: not much help Surface Area = SA of cone + SA of cylinder 2(base of cone) = rl + r + 2rh + 2r 2r = rl + r + 2rh SA = rl + r + 2rh = (12)(13) + (12) + 2(12)(10) = 156 + 144 + 240 = 540 = 1696.46

Ch 10 Coordinate Relations and Transformations SSM: y is measure of a small medium acute angle Eliminate C and D. Three angles in a triangle add to 180. Vertical angles give us Angle TRS = 180 (50+92) = 38. Angle SQT = y and shares same arc as angle TRS so they must have the same measures. y = 38. Coordinate Relations and Transformations

Ch 12 SSM: formula on formula sheet plug in values Surface Area (SA) = 2(lw + lh + wh) new height is 4 + 3.5 = 7.5 SA = 2[(18)(13.5) + (18)(7.5) + (13.5)(7.5)] = 2[479.25] = 958.5 Ch 6 Coordinate Relations and Transformations

SSM: medium acute angle Eliminate C and D Angle DAE is complementary with angle DBC. 90 36 = 54. Coordinate Relations and Transformations Ch 10 SSM: find formula on formula sheet

diameter = twice radius not much help Point on a circle much satisfy the equation of a circle. Put given information (remember radius = diameter) into equation. (x (-2))2 + (y (-2))2 = 52 (x + 2)2 + (y + 2)2 = 25 Plug points into equation and see which satisfies Coordinate Relations and Transformations Ch 10

SSM: slightly less than Circumference Arc length is found by the following proportion: 70 x --------- = --------360 C=2r 360x = 140(40) 360x = 5600

x = 48.87 Coordinate Relations and Transformations Ch 6 SSM: Angle U is medium obtuse Eliminate A, B and D A hexagon has a sum of its interior angles = 720 (from (n-2)180) 720 = 90 + 150 + 150 + 90 + x + x 720 = 480 + 2x 240 = 2x

120 = x Coordinate Relations and Transformations Ch 12 SSM: find formulas on formula sheet Cube has all sides the same (h = w = l). Volume = lwh = s3 64 = s3

4=s SA = 6s2 = 6(4)2 = 96 Coordinate Relations and Transformations Ch 6 SSM: plot points plot answers Rectangles diagonals bisect each other and are at the midpoint. Only answer A corresponds to another vertex. Use same concept as in chapter 1

finding the other endpoint. Coordinate Relations and Transformations Ch 11 SSM: greater than of a circle, but less than a circle Area of a sector solves the following proportion: 130 x

--------- = ---------360 r 130(5) = 360x 10210.18 = 360x 28.36 = x Ch 12 Coordinate Relations and Transformations SSM:

volume is a cubic relationship 27 Volume of sphere: (4/3)r3 Plug given r values in 33 = 27 and 53 = 125 125 Coordinate Relations and Transformations Ch 6

SSM: small obtuse angle eliminate C and D Once around a point is 360. Interior angle of octagon is 135 and the interior angle of a trapezoid is 125 (180 55 = 125). Angle x = 360 (135 + 125) = 360 260 = 100 Ch 10 Coordinate Relations and Transformations

SSM: find formula decipher equation Equation of a circle: (x h)2 + (y k)2 = r2 (x + 4)2 + (y 5)2 = 32 Remember negative of a negative is a positive. Center (-4, 5) Ch 12

Vol = (1/3)Bh = (1/3)(129)(8) = (1/3)864 = 288 Coordinate Relations and Transformations SSM: find formula for volume of pyramid plug in numbers Coordinate Relations and Transformations Ch 12

SSM: examine formula from formula sheet radius is a square relationship Cylindrical container volume formula: Vol = rh 4Vol = Rh setup proportion: Vol rh -------- = --------4Vol

Rh 1 r ------ = -----4 R R = 4r R = 2r