ࡱ>   V]L .bjbjPP 4::;&: :     8V\6"( # # #///1333333,>_ /.///_D6   # # tD6D6D6/\  #  #1D6/1D6D6bU$}@ma4NyV0χD6}D6 }///__D6////////////: :   Name ________________________ Period ______ Date ____________ Geometry Unit 3 Model Curriculum Assessment 1.  On the directed line segment from R to S on the coordinate plane above, what are the coordinates of the point that partitions the segment in the ratio 2 to 3 ? 2.  On the coordinate plane above,  EMBED Equation.DSMT4  represents a walking path in a park. Lights have been installed at the locations represented by points A and B. The park manager wants to place two additional lights at equal intervals from A to B. What are the coordinates of the points that represent where the new lights should be placed? 3. Point P lies on the directed line segment from  EMBED Equation.DSMT4  to  EMBED Equation.DSMT4  and partitions the segment in the ratio 2 to 1. What are the coordinates of point P ? 4. Point R lies on the directed line segment from  EMBED Equation.DSMT4  to  EMBED Equation.DSMT4  and partitions the segment in the ratio 3 to 5. What are the coordinates of point R ? 5.  In right triangle ACB above,  EMBED Equation.DSMT4  is perpendicular to  EMBED Equation.DSMT4  Complete the proof that  EMBED Equation.DSMT4  by providing a reason for each statement in the table below. StatementsReasonsTriangle ACB is a right triangle. EMBED Equation.DSMT4  is a right angle. EMBED Equation.DSMT4  is perpendicular to  EMBED Equation.DSMT4  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  are right angles. EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 6.  Triangle JKL above represents the boundary of a state wilderness area. An access road will be constructed that intersects side JK at a 90degree angle and extends to point L. The road will intersect side JK 24 miles from point K, and the length of side KL is 30 miles. Part A: What is the length, in miles, of the access road? Show your work. Part B: What is the length, in miles, of side JK ? Show your work. Part C: What is the length, in miles, of side JL ? Show your work. 7.  The figure above represents a swing set. The supports on each side of the swing set are contructed from two 12-foot poles connected by a brace at their midpoint. The distance between the bases of the two poles is 5 feet. Part A: What is the length of each brace? Part B: Which theorem about triangles did you apply to find the solution in Part A? 8. Answer Parts AD below to complete some aspects of the proof that the medians of a triangle meet at a point. Without loss of generality, we can assume that the vertices of the triangle are at the points  EMBED Equation.DSMT4   EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  as shown below.  Then the midpoints of  EMBED Equation.DSMT4   EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  can be labeled as  EMBED Equation.DSMT4   EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  respectively, as shown.  Part A: It can be shown that the coordinates of  EMBED Equation.DSMT4  are  EMBED Equation.DSMT4  and the coordinates of  EMBED Equation.DSMT4  are  EMBED Equation.DSMT4  What are the coordinates of  EMBED Equation.DSMT4  in terms of a, b, and c ? Part B: Based on your answer to Part A, what is the slope of  EMBED Equation.DSMT4  in terms of a, b, and c ? Part C: Based on your answer to Part B, what is the equation of  EMBED Equation.DSMT4  Part D: It can be shown that  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  intersect at the point  EMBED Equation.DSMT4  Show that  EMBED Equation.DSMT4  is also a point on  EMBED Equation.DSMT4  9.  Refer to parallelogram ABCD above. Complete the proof that segment AC and segment BD bisect each other by providing the missing statements or reasons in the table below. StatementsReasonsGiven EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 Corresponding parts of congruent triangles are congruentDefinition of midpointSegment AC and segment BD bisect each other 10. To find the height of a lamppost at a park, Rachel placed a mirror on the ground 20feet from the base of the lamppost. She then stepped back 4 feet so that she could see the top of the lamp post in the center of the mirror. Rachel's eyes are 5 feet 6 inches above the ground. What is the height, in feet, of the lamppost?  11. In trapezoid ACDE below,  EMBED Equation.DSMT4  is congruent to  EMBED Equation.DSMT4  the length of  EMBED Equation.DSMT4  is  EMBED Equation.DSMT4  and angle A is a right angle. What is the area of trapezoid ACDE ?  12.  EMBED Equation.DSMT4  The equation above represents the display on a calculator in degree mode. Use right triangles to explain the meaning of the equation and why it can be applied to any size right triangle with a  EMBED Equation.DSMT4  angle. 13.  For the two right triangles above, explain why  EMBED Equation.DSMT4  What trigonometric ratio is also equal to the two given ratios? 14.  In the right triangles above,  EMBED Equation.DSMT4  For each ratio of side lengths in the table below, use the right triangles to identify another ratio of side lengths that is equal to the given ratio and all sine, cosine, or tangent ratios that are also equal to the given ratio. Side RatioTrigonometric Ratios EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  15. If angle X and angle Y are complementary angles, which of the following must be true? a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c.  EMBED Equation.DSMT4  d.  EMBED Equation.DSMT4  Explain your answer using words and figures. 16.  The figure above represents a plan for a wheelchair ramp to a step that has a height of 10 inches. Jodi and Kevin each used right-triangle trigonometry to determine the length of the ramp. Both solutions are shown below. Explain why both solutions resulted in the same answer. Jodis solutionKevins solution EMBED Equation.DSMT4  EMBED Equation.DSMT4  17.  In the figure above,  EMBED Equation.DSMT4  Based on the figure, which of the following equations is also true? a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c.  EMBED Equation.DSMT4  d.  EMBED Equation.DSMT4  18. A 12-foot ladder that is leaning against a wall makes a  EMBED Equation.DSMT4  angle with the level ground. Which of the following equations can be used to determine the height, y, above the ground, in feet, that the ladder touches the wall? a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c.  EMBED Equation.DSMT4  d.  EMBED Equation.DSMT4  19.  The figure above represents a plot of land that Susan has measured to use as a fenced garden. Before she builds the fence, she wants to make sure that the plot is rectangular. She measures the length of one of the diagonals. If Susans plot is rectangular, what will be the length, in feet, of the diagonal she measured? 20. The diagram below shows a model of a staircase in which all the riser heights are equal and all the tread lengths are equal.  A carpenter wants to build a staircase in which each riser has a height of 6 inches and each tread has a length of 11 inches. Which of the following expressions is equal to the stair angle? a.  EMBED Equation.DSMT4  b.  EMBED Equation.DSMT4  c.  EMBED Equation.DSMT4  d.  EMBED Equation.DSMT4  21. Use trigonometry to show that a formula for the area of  EMBED Equation.DSMT4 below is  EMBED Equation.DSMT4   22. Which of the following expressions can be used to find the area of the triangle below? Select all that apply.  Can Be Used  EMBED Equation.DSMT4   SHAPE \* MERGEFORMAT   EMBED Equation.DSMT4   SHAPE \* MERGEFORMAT   EMBED Equation.DSMT4   SHAPE \* MERGEFORMAT   EMBED Equation.DSMT4   SHAPE \* MERGEFORMAT   EMBED Equation.DSMT4   SHAPE \* MERGEFORMAT   EMBED Equation.DSMT4   SHAPE \* MERGEFORMAT  23.  The figure above shows a triangle drawn over a map of Honduras. Use the measurements of the triangle to approximate the area, in square kilometers, of Honduras. Show your work. 24.  For  EMBED Equation.DSMT4  above, determine whether the Law of Sines or the Law of Cosines is the best method to find the value of x. Do not solve for x. Justify your answer. 25.  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