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Understanding Quadrilaterals and Trapezoids: Coordinate Geometry Review

In this chapter, we explore the properties and classifications of quadrilaterals and trapezoids, with an emphasis on finding coordinates and midsegments. You'll learn to identify various quadrilaterals, apply the Trapezoid Midsegment Theorem, and solve for unknown variables using coordinate geometry. Practice exercises and examples will help reinforce your understanding of slope, length, and relationships within these figures. Prepare for the upcoming test with comprehensive review questions focusing on essential concepts and calculations.

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Understanding Quadrilaterals and Trapezoids: Coordinate Geometry Review

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  1. Chapter 6 Review March 20, 2012 (1B, 2B) March 21, 2012 (4B)

  2. Warm-up • Get your folder and check your quiz • Practice 6-6: # 1 – 17 (odd)

  3. Warm-up

  4. Warm-up

  5. Questions on Homework/Quiz?

  6. Section 6-6/6-7: Figures in Coordinate Plane (cont’d) • Objectives: You will learn to • find coordinates of a quadrilateral (cont’d) • find midsegments of trapezoids

  7. Example 1: Use the properties of each figure to find the missing coordinates

  8. Example 2: Using the coordinates you just found, find the following: NC = CS = Slope of NC = Slope of SU =

  9. Midsegments/Medians of Trapezoids • The midsegment of a trapezoid is the segment that joins the midpoints of the nonparallel sides (legs) • Trapezoid Midsegment Theorem: • 1) The midsegment of a trapezoid is parallel to the bases. • 2) The length of the midsegment of a trapezoid is half the sum of the lengths of the bases.

  10. Example 3: Find x in Trapezoid UNCW

  11. Example 4: Find x

  12. Example 5: Find x in trapezoid ELON

  13. Example 6: a) If BG = 8, then CF = __ DE = __ b) If CF = 10, then BG = __ DE = __ c) If DE = 15 and BG = 7, then CF = __ d) If CF = 2x + 4, BG = 2x + 1, and DE = 3x + 2, then x = ___

  14. Coordinate Proofs (H)

  15. Example 8: Given: TWVU are midpoints of each side

  16. Example 9:

  17. Test Review • Define, classify and know properties of all quadrilaterals: sides, diagonals, angles • Kites • Trapezoids/Isosceles Trapezoids • Parallelograms: • Rectangle • Rhombus • Square • Classify by coordinates: using slope and length

  18. Test Review • Be able to find missing coordinates based on properties of quadrilaterals: • Using Numbers • Using Variables • Find slope and length using variables • Be able to find midsegment/median: • Length • Coordinates • Know Distance and Slope Formulas

  19. Test Review Honors • p. 339, # 1- 34 • p. 342, # 6 – 22 (even) Note: p. 339, #11, the quadrilateral should be NMKL instead of NMLK Regular • p. 339, # 1 – 32 • p. 342, # 6 – 22 (even)

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