Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x.
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1 1 Pre-AP Geometry Chapter 10 Test Review Standards/Goals: G.CO.11/ C.1.i.: I can use properties of special quadrilaterals in a proof. D.2.g.: I can identify and classify quadrilaterals, including parallelograms, rectangles, rhombi, squares, kites, trapezoids, and isosceles trapezoids using their properties. D.2.h.: I can identify and classify regular and non-regular polygons based on the number of sides, the angle measures, and the side lengths. D.2.i.: I can apply the angle sum theorem for triangles and polygons to find interior and exterior angle measures given the number of sides, to find the number of sides given angle measures, and solve real-world problems. G.SRT.5.: I can solve problems and prove relationships in geometric figures. IMPORTANT VOCABULARY Polygon Diagonals Convex polygons Concave polygons Parallelogram Quadrilateral Rectangle Consecutive angles Bases of a Legs of a Isosceles Median of a trapezoid trapezoid trapezoid trapezoid Short Answer #1. Figure ABCD is a parallelogram. What are four geometric attributes you know because ABCD is a parallelogram? Regular Interior Exterior polygon Angles Angles Rhombus Square Trapezoid Kite Coordinate proofs Slope #2. What additional pieces of information could be supplied to make ABCD a parallelogram? #3. Why is it that the statement all rhombi are squares is FALSE, but the statement all squares are rhombi is true? Explain True/False. For the following questions, write true or false. Explain false. #1. If the diagonals are perpendicular, then the quadrilateral is a rhombus. #2. If the diagonals are perpendicular, then the parallelogram is a rhombus.
2 2 #3. If diagonals are congruent, then parallelogram is a rectangle. #4. If the diagonals are congruent, then quadrilateral is a rectangle. Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x. #2. Use the figure below for parts a & b: a. In parallelogram ABCD, m<1 = x + 12, and m<2 = 6x 18. Find m<1. b. In parallelogram ABCD, m<a = 58. Find m<b #3. Find x in the trapezoid below:
3 3 #4. The length of the median of trapezoid EFGH is 13 feet. If the bases have lengths 2x + 4 and 10x 20, find x. #5. Use rhombus PQRS and the given information to find each value. a. If TR = 14, find PR. b. If m<spr = 21 degrees, find m<spq. c. Find m<rtq. d. If RQ = 5x 9 and SR = 19 + x, find the value of x. e. If <SRP = 4x + 9 and <RPQ = 2x + 27, find the value of x. #6. ABCD is a kite. If RA = 17, and BD = 12, find BA.
4 4 #7. Find x and y in the figure: Find all of the numbered angles in the figures: #8. #9. #10. #11. #12. #13. #14. If the slope of AB is ¼, the slope of BC is -5, and the slope of CD is ¼, find the slope of DA so that ABCD is a parallelogram.
5 5 #15. The length of ONE base of a trapezoid is 22 meters and the length of the median is 28 meters. Find the length of the other base. What are the coordinates of the vertices of each parallelogram? #16. #17. #18.
6 6 Classify each quadrilateral as precisely as possible. #19. #20. #21. #22. #23. #24. Give the coordinates for D and E without using any new variables. #25. Rectangle #26. rhombus #27. The figure below is a quadrilateral and segment AB is parallel to segment CD. a. Find the perimeter of the figure. b. Find the area of the figure, based on the given properties c. What would be the most specific classification of the quadrilateral? Justify your answer.
7 7 #28. Given the following theorems: If a quadrilateral is a rectangle, then its diagonals are congruent. If a quadrilateral is a rhombus, then its diagonals are perpendicular. a. Write the converse of each theorem. b. Determine whether each converse is true or false. Explain your answers. If the converse is to a theorem is false, provide an example of a quadrilateral that serves as a counterexample. #29. Can a polygon have interior angles of 110 degrees? #30. Use coordinate geometry to determine if the figure is a rhombus or not.
8 8 Multiple Choice #1. Which of the following conditions or set of conditions MUST be met for a parallelogram to be a rectangle? a. Diagonals are perpendicular b. Diagonals are congruent. c. All sides are congruent. d. The length of a diagonal is equal to the length of a side. #2. Which of the following conditions or set of conditions is sufficient for a parallelogram to be a square? a. Diagonals are perpendicular and diagonals are congruent. b. Diagonals are congruent. c. All sides are congruent d. The length of the diagonal is EQUAL to the length of a side. #3. Given: ABCD is a parallelogram with AB AD. Conclusion: ABCD is a rhombus Which corresponding reason justifies the stated conclusion? a. Opposite sides of a parallelogram are congruent. b. A quadrilateral with 2 congruent adjacent sides is a rhombus c. Opposite angles of a rhombus are congruent d. The diagonals of a parallelogram bisect each other #4. EFGH is a kite. To prove that the diagonals of a kite are perpendicular, which pair of angles must you prove congruent using CPCTC? a. <EFI & <EHI b. <GFI & <GHI c. <EIF & <EIH d. <FIE & <HIG #5. What is m<1 in this parallelogram? a. 20 b. 60 c. 80 d. 100 #6. Which reason can be used to conclude that DFGH is a parallelogram? a. There are two pairs of congruent opposite angles. b. The diagonals bisect each other. c. There are two pairs of congruent opposite sides. d. There are two pairs of opposite parallel sides.
9 9 #7. Which reason can be used to conclude that LMNO is a parallelogram? a. There are two pairs of congruent opposite angles. b. There are two pairs of congruent opposite sides. c. There are two pairs of opposite parallel sides. d. There is one pair of congruent and parallel slides. Use the rhombus TQRS to answer the next FOUR questions: #8. What is the measure of <1? a. 47 b. 37 c. 74 d. 53 #9. What is the measure of <2? a. 47 b. 74 c. 37 d. 53 #10. What is the value of x? a. 2 b. 1 c. 5 d. 4 #11. What is the value of y? a. 4 b. 3 c. 2 d. 1 #12. D.2.i.: For kite PQRS, find m<s a. 248 b. 68 c. 112 d. 124 #13. Which of the following is a property of a parallelogram? a. Each pair of opposite sides is congruent. b. Only one pair of opposite angles is congruent. c. Each pair of opposite angles is supplementary. d. There are four right angles.
10 10 #14. Which of the following is true for ALL rectangles? a. The diagonals are perpendicular b. The diagonals bisect opposite angles. c. The consecutive sides are congruent. d. The angles are all 90 degrees. #15. Which formula or formulas do you need to use to prove that if the segments connecting the midpoints of a trapezoid are joined they form a parallelogram? a. Slope formula b. Distance formula c. Distance formula and slope formula d. Slope formula and midpoint formula #16. Which formula or formulas do you need to use to prove that a quadrilateral is an isosceles trapezoid? a. Slope formula b. Distance formula c. Distance formula and slope formula d. Slope formula and midpoint formula #17. A quadrilateral that is both a rectangle and a rhombus is a. a. Quadrilateral b. Square c. Parallelogram d. Trapezoid #18. The segment joining the midpoints of the nonparallel sides of a trapezoid is called the. a. Base b. Leg c. Diagonal d. Median #19. Segments that join vertices in a quadrilateral are called. a. Diagonals b. Bases c. Legs d. Medians #20. Which of the following is a property of a parallelogram? a. The diagonals are congruent. b. The diagonals are perpendicular. c. The diagonals bisect each other d. The diagonals bisect opposite angles.
11 11 #21. What is the most accurate description of the polygon at the right? a. Rhombus b. Trapezoid c. Kite d. Quadrilateral #22. What is the most accurate description of the polygon at the right? a. Rhombus b. Square c. Rectangle d. Trapezoid #23. What kind of triangle is this? a. Right b. Equilateral c. Isosceles d. Scalene #24. Quadrilateral ABCD has diagonals that are perpendicular. It also has exactly one pair of opposite angles with equal measures. What type of quadrilateral is it? a. Square b. Rhombus c. Rectangle d. Kite #25. What type of triangle is shown at the right? a. Equilateral b. Right c. Isosceles d. Scalene
12 12 #26. What is the most accurate description of the polygon at the right? a. Rhombus b. Trapezoid c. Kite d. Quadrilateral #27. The expression (n 2)180 is used to find the sum of the interior angles of an n-sided figure. A 5-sided figure has interior angles with measures of 90 degrees, 120 degrees, 90 degrees, x degrees and y degrees. If x < y and 90 < x < 180, which inequality can be used to describe the possible degree values for y? a. 0 < y < 90 b. 120 < y < 150 c. 90 < y < 120 d. 120 < y < 240 #28. Quadrilateral TRAP is shown at the right. Which of the following could you use to show that TRAP is a trapezoid? a. Prove RA = TP b. Prove RA AP c. Prove TR PA d. Prove that there are no right angles formed by the line segments.
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