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Name: Geometry Date: Problem Solving Geometry June 2011 Assignment 1. Points M, N, and X are collinear and X is between M and N. If MN = 28 and the ratio between MX and NX is 3:4, find the length of . 2. Point Q is between points P and R on the value of x. . If PR = 82, PQ = 4x - 304 and RQ = 4x - 262, find 3. Ms. Barcenas said, "If you know one vertical angle, you know three other angles." What did she mean by this? 4. E is the midpoint of 5. Isabella was cleaning up a big mess. A forklift operator accidentally dropped a large load of carpenters' squares (which are actually triangles). They were all over the place. Some were shaped like equilateral triangles (they were defective), and others were shaped like isosceles triangles. Is this a good classification system for Isabella to use to begin sorting them back into their proper piles? Explain. Can you think of a better one? . If DE = 4x + 10 and EF = 62, find the value of x. PROBLEM SOLVING GEOMETRY 1 [Type text] [Type text] 6. CD m EF AGC = (3x + 12) m FHB = (2x + 21) Find the value of x. 7. B is in the interior of If m m ADC = (9x - 59) , ADB = (2x + 10) , and m BDC = (x + 45) , find the value of x. 8. ADC. [Type text] Name: Geometry Date: Luis and Alyssa were playing a learning game in which they had to virtually sort points, lines, and planes from a collection of points that appeared on an electronic game board. For a correct response, the board flashed green. If an incorrect response was given, or if a duplicate of a previous response was offered, the board would buzz and flash red. Pretend you are playing the game and using the points below. Name 3 points, 3 lines, and 3 planes. Note: The points do not all necessarily lie in the same plane. 9. As shown in the figure, you can create a pyramid by folding sides of a piece of paper up and then use masking tape to hold it together. Of the five planes containing sides of the pyramid, which two planes do not intersect? A. B. C. D. E. 1 and 4 1 and 5 2 and 5 2 and 4 All planes intersect. PROBLEM SOLVING GEOMETRY 3 [Type text] [Type text] [Type text] 10. Why are points, lines, and planes considered fundamental objects in geometry? 11. Is it possible for a bisector to divide a line into unequal parts? Explain. 12. Suppose M is between L and N. LM = (2 1/2y + 3), MN = (2y + 7/2), LN = 123. Find the value of y. 13. Find a set of objects in the room such that each set contains something represented by one point, one line, and one plane. How many such sets are there? 14. In the figure, and m Find m , , DBC=26 . ABE. 15. A triangle is the figure formed by the union of three segments determined by ___________. A. B. C. D. E. F. three skew points three angels three collinear points any three points three noncollinear points three rays 16. Find the distance between the two points. Name: Geometry Date: (a) G(5, 8), H(6, -7) (b) M(5, -8), N(-3, 3) (c) P(-1, 1), Q(-7, -8) 17. E is the midpoint of . If DE = 3x + 9 and EF = 6x - 6, then DF = ______. 18. If m UVW = m XYZ, then ______. Points U, V, W, X, Y, and Z are coplanar. UVW and UVW UVW and XYZ form a straight angle. XYZ XYZ are adjacent angles. 19. The distance between two points is the ___________ of the ___________ joining the points. A. B. C. D. E. measure, complementary angle length, segment length, ray measure, supplementary angle radius, circle 20. Two angles are complements. 34 Find the measures of the two angles. less than twice the larger angle equals twice the smaller angle. 21. If Ms. Cordova cuts a cake into slices (through the center of the cake) that have a vertex angle of 20°, how many such whole slices can be made from half a cake? 22. Which of the following statements is NOT true? PROBLEM SOLVING GEOMETRY 5 [Type text] [Type text] [Type text] A. Planes X and Y contain both M and N. B. Plane Y and intersect in point L. C. Points L, M, N, and P are coplanar. D. Points N and P are noncoplanar. 23. Line AB is a transversal of line CD and line EF. Circle which of the following is true? BHE is the supplement of EHG is the supplement of DGA is the supplement of DGA is the complement of DGA DGH FHB EHG None of the above 24. How many endpoints are required to define the locations of 7 different rays and 5 different lines such that no rays or lines share any common point with any other rays or lines? Name: Geometry Date: 25. Is it possible for two angles located on different parts of the surface of the earth to be complementary? Explain. PROBLEM SOLVING GEOMETRY 7 [Type text] [Type text] [Type text] Name: Geometry Date: PROBLEM SOLVING GEOMETRY 9