1. Pretest Please complete the pretest for this standard on your own. Try to remember all you can from our first discussion of this topic.

2. Prove theorems involving quadrilaterals. MA.912.G.3.4

3. LEQ: How do I prove theorems involving quadrilaterals? Theorems about Parallelograms If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

4. LEQ: How do I prove theorems involving quadrilaterals? Theorems about Rhombuses, Rectangles, Trapezoids, and Kites If a parallelogram is a rhombus, then its diagonals are perpendicular. If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. If a parallelogram is a rectangle, then its diagonals are congruent. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. If a quadrilateral is a trapezoid, then (1) the midsegment is parallel to the bases, and (2) the length of the midsegment is the average of the lengths of the bases. If a quadrilateral is a kite, then its diagonals are perpendicular.

5. I do… How can you determine, without measuring any angles, whether a quadrilateral is a rectangle? Measure to show diagonals bisect each other. This makes the quadrilateral a parallelogram. The measure to show that diagonals are congruent. This makes the parallelogram a rectangle.

6. I do… Determine whether a quadrilateral is a parallelogram. Since angle C is supplementary to both angle A and angle D, quadrilateral ABCD is a parallelogram.

7. Sage and Scribe We do…

8. Each pair of students will need only one paper. Student A will write down a theorem about quadrilaterals and pass it to their should partner. Student B will review Student A’s property, coach or praise their work, and write a theorem of their own. Then pass the paper back to Student A and repeat the process until time is called. The pair of students with the most correct wins!

9. You do…

13. Post Test Please complete the post test for this standard on your own. Do the best you can, hopefully you will show improvement over your pretest score.