1. 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) 5.1 warm-up 6 -3 -2 -1 0 1 2 3 x -3 1 2 3 y

2. 6.3 Proving that a Quadrilateral is a Parallelogram Pardekooper

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

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

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

6. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram, Pardekooper

7. If the one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram. Pardekooper

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

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

10. Just one more problem A B C D m + 9. 1 4 k - 3. 5 2. 6 k m ABCD is a parallelogram. Solve for m & k. m+9.1 = 4k-3.5 m = 2.6k substitution 2.6k+9.1 = 4k-3.5 - 4k - 4k -1.4k+9.1 = -3.5 - 9.1 - 9.1 -1.4k = -12.6 -1.4 -1.4 k = 9 m = 2.6(9) m = 23.4 Pardekooper

11. And now the assignment. Pardekooper

12. Assignment Workbook Page 361 all