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

2. Squares, Rectangles, and Rhombi Statements and Converses One Big FigureRectangles and Rhombi Grab Bag Review! 200 400 600 800 1000 Bonus Question: 5000 pts

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.

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.

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.

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.

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.

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

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

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

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

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.

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

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

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

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

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

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.

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.

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

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

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

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.

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.

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.

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.

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.

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 ∠ XAN are all 90˚ because of alternate interior angles. Thus, JANE is a rectangle.

29. 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. 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!