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Squares, Rectangles, and Rhombi!

Questions from McDougal Littell , Geometry, 2007. Squares, Rectangles, and Rhombi!. Squares, Rectangles, and Rhombi. Topic 1: 200. Question: Is the statement true? What about its converse? If a quadrilateral is a rectangle, then it is a parallelogram. Answer

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Squares, Rectangles, and Rhombi!

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  1. Questions from McDougal Littell, Geometry, 2007. Squares, Rectangles, and Rhombi!

  2. Squares, Rectangles, and Rhombi

  3. Topic 1: 200 • Question: • Is the statement true? What about its converse? • If a quadrilateral is a rectangle, then it is a parallelogram. • Answer • A rectangle is always a parallelogram, but a parallelogram isn’t necessarily a rectangle. Back

  4. Topic 1: 400 • Question: • Is the statement true? What about its converse? • If a quadrilateral is a parallelogram, then it is a rhombus. • Answer • A parallelogram isn’t necessarily a rhombus, but a rhombus is always a parallelogram. Back

  5. Topic 1: 600 • Question: • Is the statement true? What about its converse? • If a quadrilateral is a square, then it is a rhombus. • Answer • A square is also a rhombus, but a rhombus isn’t necessarily a square. Back

  6. Topic 1: 800 • Question: • Is the statement true? What about its converse? • If a quadrilateral is a rectangle, then it is a rhombus. • Answer • A rectangle isn’t necessarily a rhombus, and a rhombus isn’t necessarily a rectangle. Back

  7. Topic 1: 1000 • Question: • If a statement and its converse are true, how can you make a new statement which incorporates both? • Answer • If a statement and its converse are both true, then it is a biconditional statement. You can reword it into an “if and only if” statement to show that both “sides” hold. Back

  8. Topic 2: 200 • Question: • BGED is a rectangle and ABCD is a rhombus, find the measure of ∠GDB • Answer • m∠GDB = 27˚ Back

  9. Topic 2: 400 • Question: • BGED is a rectangle and ABCD is a rhombus, find the measure of ∠ABC • Answer • m∠ABC = 54˚ Back

  10. Topic 2: 600 • Question: • BGED is a rectangle and ABCD is a rhombus, find the measure of ∠DAB • Answer • m∠DAB = 126˚ Back

  11. Topic 2: 800 • Question: • BGED is a rectangle and ABCD is a rhombus, find the measure of ∠GCE • Answer • m∠GCE = 126˚ Back

  12. Topic 2: 1000 • Question: • BGED is a rectangle and ABCD is a rhombus. • List all of the triangles which are congruent in the figure. • Answer • ΔABH, ΔADH, ΔCHD, ΔCBH, and the bottom triangles with hypotenuses of CG and CE are all congruent. Back

  13. Topic 3: 200 • Question: • Find m∠URV • Answer • m∠URV = 71˚ Back

  14. Topic 3: 400 • Question: • Find the length of RT. • Answer • Length RT = 28.65 Back

  15. Topic 3: 600 • Question: • Find m∠RVT • Answer • m∠RVT = 38˚ Back

  16. Topic 3: 800 • Question: • Find m∠XWO • Answer • m∠XWO = 34˚ Back

  17. Topic 3: 1000 • Question: • Find the length of WZ. • Answer • Length WZ = 18.45 Back

  18. Topic 4: 200 • Question: • Classify the quadrilateral and then solve for ‘x’ and ‘y’. • Answer • The quadrilaterals is a square, while x = 4 and y = 9. Back

  19. Topic 4: 400 • Question: • Classify the quadrilateral, and then solve for ‘x’ and ‘y’. • Answer • The figure is a rhombus, while x = 5 and y = 11. Back

  20. Topic 4: 600 • Question: • Draw the figure, and then solve • Answer • Length XY = 11 Back

  21. Topic 4: 800 • Question: • Draw the figure and then solve. • Answer • m∠Y = 60˚ Back

  22. Topic 4: 1000 • Question: • Draw the figure and then solve. • Answer • Length WY = 10 Back

  23. Topic 5: 200 • Question: • Answer • The slope of MN is (3/11) and PQ is (3/11), while the slope of MQ is (-5/4) and NP is (-5/4), so there are two pairs of parallel sides, so the MNPQ is a parallelogram. Back

  24. Topic 5: 400 • Question: • Answer • The distances of MN and PQ are 11.4, while the distances of NP and MQ are 6.4, so there are two pairs of congruent sides, meaning MNPQ must be a parallelogram. Back

  25. Topic 5: 600 • Question: • Answer • Because the diagonals are bisected, set 12x + 1 = 49 and 8y + 4 = 36. This gives x = 4 and y = 4. Back

  26. Topic 5: 800 • Question: • Answer • Let x = the first angle, and y = the adjacent angle. Recognize that x = 3y – 12 and y = 180 – x. Plugging in, one gets x = 132, so y = 48. One of the other interior angles is also 132, and another is 48. Back

  27. Topic 5: 1000 • Question: • Answer • The polygon has 5 sides; the interior angles sum to 540, and as always, the exterior angles sum to 360. Back

  28. Bonus Question: 5000 pts. • Question: • Can claim that JANE is a more specific type of quadrilateral? Explain. • Answer • Because JANE is a parallelogram, we already know its opposite sides are congruent. To show the angles of JANE are all 90, note that because JXPE is a parallelogram and XP is perpendicular to EN, PX is also perpendicular to JA. This implies that m∠PEA, m∠XJE, m∠PNA, and m∠XANare all 90˚ because of alternate interior angles. Thus, JANE is a rectangle. Back

  29. Daily Double Write down how much money you are willing to risk. If you get the question right, you win that money; if you get it wrong you lose it!

  30. Daily Double Write down how much money you are willing to risk. If you get the question right, you win that money; if you get it wrong you lose it!

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