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Altitudes, Medians, Perpendicular Bisectors, and Parallel Line Theorem Review Activity

Altitudes, Medians, Perpendicular Bisectors, and Parallel Line Theorem Review Activity. November 17, 2011. Points. 3 – First answer done completed correctly 1 – To all groups who had the correct answer but was not first one completed Bonus Round:

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Altitudes, Medians, Perpendicular Bisectors, and Parallel Line Theorem Review Activity

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  1. Altitudes, Medians, Perpendicular Bisectors, and Parallel Line Theorem Review Activity November 17, 2011

  2. Points 3 – First answer done completed correctly 1 – To all groups who had the correct answer but was not first one completed Bonus Round: Teams work together to solve the problem. Each team must wager 1, 2, 5, or 10 points. So answer correct you receive those points, if it is incorrect you loose those points

  3. 1 Find the Value of x — = x — = 34 X = 17

  4. 2 Find the Value of x = = 7 — 2x — X = 7

  5. 3 Find the Value of x = — x - 8 — = 35 X = 25.5

  6. 4 Find the Value of x — = 3x — = 4x+20 X = 10

  7. 5 X = — A B = — = = — — Y Z C YZ AB is parallel to ______ BC is parallel to ______ XY

  8. 6 X = — A B = — = = — — Y Z C If AC = 3x+1, and XZ=10x-6 Then AC=____ 7

  9. Bonus 1 6 X = — A B = — = = — — Y Z C 5 If CB=x-1, and XY=3x-7 then XY=_____ If angle XYZ=48, then angle XAB=_____ If angle XBA=37, then angle XZY=_____ 48 37

  10. 7 parallel If three ________ lines cut off ___________ segments on one ___________, then they cut off _________ segments on every __________. congruent transversal congruent transversal

  11. 8 What is a segment from the vertex of the triangle to the midpoint of the opposite side? Median

  12. 9 What is the definition of an Altitude? The perpendicular segment from a vertex of the triangle to the segment that contains the opposite side.

  13. 10 A line that contains the ___________ of one side of a triangle and is _________ to another side passes through the _________ of the third side. midpoint parallel midpoint

  14. 11 What is a line that is perpendicular to asegment at its midpoint and does NOT have to start at a vertex? Perpendicular Bisector

  15. 12 The segment that joins the midpoint of two sides of a triangle…. 1) 2) Is parallel to the third side Is half as long as the third side

  16. Bonus 2 Definition of a Centroid The point where all three medians meet Altitude fact about right triangles Two of the altitudes of are the legs of the triangle Altitude fact about obtuse triangles Two of the altitudes are outside of the triangle

  17. 13 Error Section!! If M is the midpoint of XY and MN is parallel to YZ, then line MN is the altitude. If M is the midpoint of XY and MN is parallel to YZ, then N is the midpoint of XZ

  18. 14 10 18 12 22 20

  19. 15 Both blue lines are a good representation of altitudes. — Both blue lines are a good representation of medians NOT altitudes. — = =

  20. 16 Both lines are a good representation of Perpendicular Bisectors. The orange line are a good representation of Perpendicular Bisectors. The green line is not able to be determined. — —

  21. 17 These three lines are a good representation of Medians. The teal line is a good representation of a Median. The blue and red lines are good representations of Altitudes.

  22. 18 The intersection of AF, BE, and CD is the centroid. No it is not the centroid. Centroids are formed from medians. Altitudes are displayed here.

  23. Bonus 3 MN is the perpendicular bisector of XY, XZ, and YZ. If M is the midpoint of XY and N is the midpoint of XZ, then MN || YZ and MN = 1/2 YZ.

  24. 19 B What is the red line an example of? Explain your answer. A C A Median

  25. 20 B What is the red line an example of? Explain your answer. A D C An Altitude

  26. M N L 21 What is the black line an example of? Explain your answer. A Perpendicular Bisector

  27. 22 Why are these true? If MN = 6, then YZ = 12. If YZ = 20, then MN = 10. Just needs an explanation

  28. 23 What is the red line an example of? Explain your answer. Altitude, Median, and Perpendicular Bisector

  29. 24 What is the yellow line an example of? Explain your answer. None, explain

  30. Bonus 4 B A What are each of these lines? Explain. C Red is Altitude, orange is Median, and grey is Perp. Bisector

  31. 25 J What is the length of JK? You will be asked to justify your answer. R 3 4 K S JK = 6

  32. 26 Construct a Right Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector. Be ready to justify your answer.

  33. 27 Construct an Acute Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector. Be ready to justify your answer.

  34. 28 Construct an Obtuse Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector. Be ready to justify your answer.

  35. 29 = = 12 — K Find JK. Be ready to justify your answer. — J JK = 24

  36. 30 = = 10x — K Find x. Be ready to justify your answer. 15x +15 — J X = 3

  37. Bonus 5 Construct a Centroid. Be ready to justify your answer.

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