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WARM-UP Worksheet in Packet

WARM-UP Worksheet in Packet. You MUST plot the quadrilateral for credit!!!. YES, PARALLELOGRAM. YES, PARALLELOGRAM. Quadrilaterals in the Coordinate Plane. I can find the slope and distance between two points

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WARM-UP Worksheet in Packet

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

  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 Step 1 Show that EG and FH are congruent. Since EG = FH, Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

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

  5. Example: Verifying Properties of Squares Since EG and FH have the same midpoint, they bisect each other. 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.

  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. Your Turn: Verifying Properties of Squares Step 1 Show that SV and TW are congruent. Since SV = TW, 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.

  8. Your Turn: Verifying Properties of Squares Step 2 Show that SV and TW are perpendicular. Since 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.

  9. Your Turn: Verifying Properties of Squares Step 3 Show that SV and TW bisect each other. Since SV and TW have the same midpoint, they bisect each other. 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. The diagonals are congruent perpendicular bisectors of each other. Therefore, the quadrilateral is a SQUARE.

  10. 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 The diagonals are congruent perpendicular bisectors of each other.

  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? You MUST plot the quadrilateral for credit!!! B C A D

  12. AB and DC are parallel BC and AD are parallel 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 Therefore the quadrilateral is a Parallelogram. Slope of Slope of Slope of Slope of

  13. AB and BC are NOT perpendicular. (slopes are not opposite reciprocals) 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 Slope of Therefore the quadrilateral is NOT a rectangle or square. Slope of Slope of

  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 3. 2.

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