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5.1 warm-up

5.1 warm-up. Suppose the line shown is translated 2 units to the left and 1 unit down. Which point would lie on the translated line ? a. (-2,-2) b. (-1,1) c. (0,2) d. (2,3). y. 3. 2. 1. -3 -2 -1 0 1 2 3 x. -3. 6. Pardekooper.

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5.1 warm-up

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  1. 5.1 warm-up Suppose the line shown is translated 2 units to the left and 1 unit down. Which point would lie on the translated line ? a. (-2,-2) b. (-1,1) c. (0,2) d. (2,3) y 3 2 1 -3 -2 -1 0 1 2 3 x -3 6

  2. Pardekooper 6.3 Proving that a Quadrilateral is a Parallelogram

  3. Pardekooper What makes a quadrilateral a parallelogram? • 1. Opposite sides are congruent • 2. Opposite angles are congruent • 3. Diagonals bisect each other

  4. Pardekooper Now, we look at some theorems • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  5. Pardekooper Now, we look at some theorems • If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  6. Pardekooper Now, we look at some theorems • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram,

  7. Pardekooper Now, we look at some theorems • If the one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.

  8. A B Pardekooper D C Lets try a proof • Given: ABDCDB, BDADBC, AC • Prove: ABCD is a parallelogram ABDCDB, BDADBC AC • Given ABD+CBDCDB+ADB Addition ABCD is a parallelogram If opposite ’s  , then parallaogram

  9. A B D C Pardekooper OK, here comes a problem. ABCD is a parallelogram. Solve for X & Y. 3Y = Y+2 3X = X+3.2 - 1X - 1X - 1Y - 1Y 2X = 3.2 2Y = 2 Y+2 2 2 2 2 3X 3Y Y = 1 X = 1.6 X+3.2

  10. A B D C Pardekooper Just one more problem ABCD is a parallelogram. Solve for m & k. m = 2.6k m+9.1 = 4k-3.5 m = 2.6(9) 2.6k+9.1 = 4k-3.5 - 4k - 4k m = 23.4 2.6k -1.4k+9.1 = -3.5 substitution m+9.1 m - 9.1 - 9.1 -1.4k = -12.6 substitution -1.4 -1.4 4k-3.5 k = 9

  11. Pardekooper And now the assignment.

  12. Assignment Workbook Page 361 all

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