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# 2012 2013 portfolio math! -ms.bush 2

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Math project end of year 10th grade

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### 2012 2013 portfolio math! -ms.bush 2

1. 1. By: Dancayra Rosario
2. 2. Question 1 :Which point is on the line 4y-2x=0A) (-2, -1)B) (-1,2)C) (1.2)D) (-1,-2)Unit 1: Points, lines, planesAnswer: 14(-1)-2(-2)=0-4+4=0
3. 3. Question 2 :If line segment AB is contained in planeP, and line segment AB is perpendicular toplane R which statement is true?A) line segment AB is parallel to plane RB) Plane P is parallel to plane RC) Line segment AB is perpendicular toplane PD) Plane P is perpendicular to plane RUnit 1: Points, lines, planesAnswer: DBecause Line segment AB is perpendicular to plane R and line segment AB is in planeP
4. 4. UNIT 2: TRIANGLES PROPERTYQuestion 1:ABC≅ XYZ•All 3 sides are congruent•ZX = CA (side)•XY = AB (side)•YZ = BC (side)•The Side Side Side postulate, thetriangles are congruent.
5. 5. UNIT 2: TRIANGLES PROPERTYQuestion 2:△ABC≅△XYZ Two sides and the included angle are congruent AC = ZX (side) ∠ACB = ∠XZY (angle) CB = ZY (side)The Side Angle Side postulate, the triangles are congruent.
6. 6. If AB ≅ CD, which statement could always beproven?1) AC ≅ DB2) AE ≅ ED3) AB ≅ BC4) EC ≅ EAIn AED with ABCD shown in the diagrambelow, EB and EC are drawn.Question 1:Answer: 1AB = CDAB+BC = CD+BCAC = BD
7. 7. Question 2:In the diagram below of triangle PRT, Q is a pointon segment PR, S is a point on segment TR, segmentQS is drawn, and angle RPT is congruent to angle RSQ.Which reason justifies the conclusion thatPRT ∼ SRQ?1) AA2) ASA3) SAS4) SSSAnswer: 1 because there are only 2 anglesand no sides
8. 8. Unit 4:QuadrilateralsQuestion 1:The opposite sides of a parallelogram arerepresented by2x + 10 and 5x - 20.Find the length of the side of the parallelogramrepresented by 4x - 1.Work:5x-20=2x+10+20 +20 4(10)-15x=2x+30 40-1-2x -2x length= 393x=303X=10The answer is 39 becausesince the quadrilateral is arectangle there are 2 pairs ofcongruent sides so I set the topand bottom to equal each otherto get X and plugged it in to theside that we had to solve.
9. 9. Unit 4:QuadrilateralsQuestion 2:Which statement describe the properties of a trapezoid?a. The bases are parallel.b. The diagonals are congruent.c. The opposite angles are congruent.d. The base angles are congruent. Answer: A The answer is A becausethe bases of a trapezoidare parallel the diagonalsare not congruent
10. 10. UNIT 5: TRANSFORMATION Question 1:In the diagram shown triangle ABC is plottedon the graph triangle ABC’ is also plotted after thetranslation of (-5,6) what will the coordinates oftriangle ABC’’ after a rotation of 180 degree?Answer:A’’ (-4,1)B’’(-4.3)C’’(-1,3)These are the answers because whenyou do a rotation of 180 coordinates(A.B) turns into coordinates (-A,-B)
11. 11. UNIT 5: TRANSFORMATION Question 2:What are the coordinates oftrapezoid ABCD after atranslation of (-2,-3)?C’ D’A’ B’CDA BA(2,1) A’(-1,1)B(4,1) B’(1,-1)C(1,4) C’(-2,2)D(5,4) D’(2.2)In order to find The coordinates of theof the trapezoid after the translationyou needed to subtract 2 from the riseof each point and subtract 3 from therun of each point.
12. 12. UNIT 6:CIRCLES Question 1: Find the value of x. Segment AB is a tangent Solution: x is a radius of the circle. Since x contains B, and AB is a tangent segment, x must be perpendicular to AB (the definition of a tangent tells us that). If it is perpendicular, the triangle formed by x, AB, and CA is a right triangle. Use the Pythagorean theorem to solve for x. 152 + x2 = 172 x2 = 64 x = 8
13. 13. UNIT 6:CIRCLESQuestion 2:In the accompanying diagram ofcircle O, m<ABC= 2x and measure arc AC= x+60Find the value of x.Work:2(2X)=X+604X=X+60-X -X3X=603X=20In order to find X you have to set <ABC times 2 and put it equal to X+60 andsolve it
14. 14. UNIT 7: SURFACE AREA ANDVOLUME Question 1:The rectangular prism shown below has a lengthof 3.0 cm, a width of 2.2 cm, and a height of 7.5 cm2.2cm3 cm 7.5cmWhat is the surface area, in squarecentimeters?1) 45.62) 49.53) 78.04) 91.2Answer: 4SA = 2lw+2hw+2lhSA= 2(3)(2.2)+2(7.5)(2.2)+2(3)(7.5) = 91.2The answer is 4 becauseyou had to substitute thelength width and heightin order to find theanswer
15. 15. UNIT 7: SURFACE AREA ANDVOLUME Question 1:Find the volume, in cubic, of the rectangular prismshown below. Answer:V = lwh10⋅2⋅4 =8010 cm4cm2 cmFinding the answer for thisproblem is easy as long thatyou know the formula whichis length times width timesheight you substitue it andyou get the pruduct
16. 16. EXTRA CREDIT!!!!2 Locus problems1 Translation problemAngle triangle properties
17. 17. LOCUSA B26 MILESPoint A and point B are 26 miles apart. How many points are 20 miles frompoint A and 22 miles from point B?Answer:2 pointsThere are 2 points from 20 miles from Ato 22 miles from B because the 2 circlesintersect at only 2
18. 18. LOCUSPlot all the points 3 unitsaway from the orgin and plotthe points 2 units away fromThe line X=1, state theCoordinates and the amountOf points of the locus’s.3 points(-1,-3)(-1,3)(3,0)
19. 19. What is the image of the point underthe translation ?A) (-9,5)B) (-8,6)C) (-2,-2)D) (-15,-8)Translation (extra)Answer:C (-2,-2)-5+3=-2 2+-4=-2
20. 20. Find the measure of angle C.M<A=120M<B=34M<A + M<B + M<C = 180120+34+M<C=180154+M<C=180M<C=26Angle Properties of TrianglesAnswer:M<C=26The answer is 26 because since awhole triangle is 180 degreesand there are 2 angles that havea measure which is m<A=120and m<B=34 so that means that120+34 equals 154 and 180-154equals 26