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Math project end of year 10th grade

Math project end of year 10th grade

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- 1. By: Dancayra Rosario
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. EXTRA CREDIT!!!!2 Locus problems1 Translation problemAngle triangle properties
- 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. 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. 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. 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

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