Unit 3 B Outcome Assessment Pythagorean Triple a set of three nonzero whole numbers that satisfy the Pythagorean Theorem

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Scot Robertson
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1 a Pythagorea Theorem c a + b = c b Uit Outcome ssessmet Pythagorea Triple a set of three ozero whole umbers that satisfy the Pythagorea Theorem If a + b = c the the triagle is right If a + b > c the the triagle is acute If a + b < c the the triagle is obtuse Triagle Triagle hypoteuse = leg leg = hypoteuse hypoteuse = short leg log leg = short leg short leg = hypoteuse log leg short leg = 60 si opposite hypoteuse Trigoometric Ratios cos adjacet hypoteuse opposite ta adjacet Iverse Trig Fuctios If si = x the si x = m If cos = x the cos x = m If ta = x the ta x = m

2 Uit 4 Picture Theorem/Postulate Relatioship/Symbols etral gle: The measure of a cetral agle is equal to its mior m O m arc. O Iscribed gle: If a agle is iscribed i a circle, the the measure of the agle equals oe-half the measure of its itercepted arc. m m If a iscribed agle of a circle itercepts a semicircle, the agle is a right agle. is a right agle. If a quadrilateral is iscribed i a circle, the its opposite agles are supplemetary. ad are supplemetary. O P R If a lie is taget to a circle, the it is perpedicular to the radius draw to the poit of tagecy. The coverse is also true. PT OR T O R P T I a circle, two cogruet chords are equidistat from the ceter of the circle. PO RO T I a circle, or i cogruet circles, two mior arcs are cogruet iff their correspodig chords are cogruet. rc dditio: The measure of a arc formed by two adjacet arcs is the sum of the two arcs. m m m

3 T V Give: is a diameter ad T is a chord If T the TV V ad T. If, the. ad are taget to the circle S T U Pythagorea Theorem: m S TU ad are taget to the circle a c b x a + b = c = = 80 x m is taget to the circle m ad are taget to the circle m

4 istace: oordiate Plae d = ( x y x ) ( y ) istace: Number Lie a b PQ = b a or a b Slope: m = y y x x Ways to Prove Two Triagles ogruet. Side-Side-Side ogruece (SSS). Side-gle-Side ogruece (SS). gle-side-gle ogruece (S) 4. gle-gle-side ogruece (S) 5. Hypoteuse-Leg ogruece (HL) Uit 4 Part Midpoit: oordiate Plae x x y y M =, ircle Stadard quatio: I the coordiate plae, the stadard equatio of a circle with ceter (h, k) ad radius r is: ( x h) ( y k) r Pythagorea Theorem: a + b = c O the coordiate plae: If a lie segmet has edpoits (x, y ) ad (x, y ) ad a partitio poit P will separate the lie segmet ito a ratio of m:, the to fid the coordiates of P. ( mx + x m +, my + y m + ) omplete the Square. Rearrage your equatio so the x s are grouped, the y s are grouped, ad the costats are o the other side of the equatio. (square term first the liear term). reate a space to complete the square for the x s ad the y s. (remember to balace both sides of the equatio). omplete the square for the x s ad y s. Fid each missig value by takig half of the middle term of each triomial, the square it. This value will always be positive. 4. Simplify by factorig your x s, y s, ad combiig like terms. a b c ostructio: opyig a Segmet ostructio: isectig a segmet ostructio: Perpedicular to a Lie Through a Poit Not o the Lie ostructio: Perpedicular isector

ostructio: opyig a gle ostructio: isectig a gle

ostructio: quilateral Triagle Iscribed i a ircle

quilateral Triagle ircumscribed about a ircle

5 ostructio: Parallel Lies ostructig the Perpedicular to a Lie Through a Poit o the Lie ostructio: opyig a gle ostructio: isectig a gle ostructio: Regular Hexago Iscribed i a ircle ostructio: quilateral Triagle Iscribed i a ircle ostructio: Square Iscribed i a ircle ostructio: quilateral Triagle ircumscribed about a ircle ostructio: ircle Iscribed i a Triagle ostructio: ircle ircumscribed about a Triagle

6 Perimeter: dd all side legths Uit 5 Part ircumferece: = πr or = πd R rc Legth: θ arc legth = 60 circumferece Rectagle: = bh Trapezoid: = h(b + b ) Parallelogram: = bh Rhombus: = d d Triagle: = bh ircle: = πr Sector: θ 60 = area of sector area of circle Regular Polygo: gles of ovex Polygos Iterior gle xterior gle Sum S = 80( ) 60 o = Pa 80( ) Oe gle ivide sum by ivide sum by 60 Shape Lateral rea Uit 5 Part Surface rea Volume ylider L = rh S = L + r or S = πrh + πr V = h or V = πr h Prism L = Ph S = L + or S = Ph + V = h Pyramid L = ½ Pl S = L + or S = ½ Pl + V = h oe L = rl S = L + r or rl + r V = h or V = Sphere S = 4 r 4 V = r Hemisphere L = πr S = r V = r r h

Math III-Formula Sheet

Math III-Formula Sheet Statistics Z-score: Margi of Error: To fid the MEAN, MAXIMUM, MINIMUM, Q 3, Q 1, ad STANDARD DEVIATION of a set of data: 1) Press STAT, ENTER (to eter our data) Put it i L 1 ) Press