1. WARM-UP Worksheet in Packet YES, PARALLELOGRAM You MUST plot the quadrilateral for credit!!!

2. Quadrilaterals in the Coordinate Plane I can find the slope and distance between two points I can use the properties of quadrilaterals to prove that a figure in the coordinate plane is a parallelogram, rhombus, rectangle, square, or trapezoid.

3. Example: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other. Step 1 Show that EG and FH are congruent. Since EG = FH,

4. Example: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other. Step 2 Show that EG and FH are perpendicular. Since,

5. Example: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other. Step 3 Show that EG and FH are bisect each other. Since EG and FH have the same midpoint, they bisect each other.

6. Example: Verifying Properties of Squares Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other. The diagonals are congruent perpendicular bisectors of each other. Therefore, the quadrilateral is a SQUARE.

7. The vertices of square STVW are S(–5, –4), T(0, 2), V(6, –3), and W(1, –9). Show that the diagonals of square STVW are congruent perpendicular bisectors of each other. Your Turn: Verifying Properties of Squares Step 1 Show that SV and TW are congruent. Since SV = TW,

8. The vertices of square STVW are S(–5, –4), T(0, 2), V(6, –3), and W(1, –9). Show that the diagonals of square STVW are congruent perpendicular bisectors of each other. Your Turn: Verifying Properties of Squares Step 2 Show that SV and TW are perpendicular. Since

9. The vertices of square STVW are S(–5, –4), T(0, 2), V(6, –3), and W(1, –9). Show that the diagonals of square STVW are congruent perpendicular bisectors of each other. Your Turn: Verifying Properties of Squares The diagonals are congruent perpendicular bisectors of each other. Therefore, the quadrilateral is a SQUARE. Step 3 Show that SV and TW bisect each other. Since SV and TW have the same midpoint, they bisect each other.

10. The diagonals are congruent perpendicular bisectors of each other. Step 3 Show that SV and TW bisect each other. Since SV and TW have the same midpoint, they bisect each other. Check It Out! Example 3 Continued

11. Example Given points: A(0,2) B(3,6) C(8,6) D(5,2) How can we prove ABCD is a parallelogram, rectangle, rhombus, or a square? CB DA You MUST plot the quadrilateral for credit!!!

12. Example A(0,2) B(3,6) C(8,6) D(5,2) Step 1: Is ABCD a parallelogram? *check to see if slopes are parallel Slope of AB and DC are parallel BC and AD are parallel Therefore the quadrilateral is a Parallelogram.

13. Example A(0,2) B(3,6) C(8,6) D(5,2) Step 2: Is ABCD a rectangle or a square? *were the slopes perpendicular? Slope of AB and BC are NOT perpendicular. (slopes are not opposite reciprocals) Therefore the quadrilateral is NOT a rectangle or square.

14. Example A(0,2) B(3,6) C(8,6) D(5,2) Step 3: Is ABCD a rhombus? *check the lengths OR…use Pythagorean Theorem. AB and BC are equal lengths Therefore the quadrilateral is a Parallelogram AND a Rhombus.

15. Now complete the “Quadrilaterals in the Coordinate Plane” Worksheet. Hint: # 6-9 could be ANY Quadrilateral. What kind of quadrilateral is it if BOTH sides are not parallel? Be as specific as possible.

16. Checkpoint 2. 3.