1. Warm Up: Day 2
Find the coordinates of point M in parallelogram PRAM.
M(__, __)
A(b, c)
M(b-a,c) . P
R(a, 0)

2. Determine the values of the variables for which, the figure
to the right is a parallelogram.
X=6, y=3

3. 2. No
3. yes alternate interior angles converse, opposite sides are parallel,
4. yes opposite sides are congruent and parallel,
5. yes opposite sides are congruent,
yes, base angles are congruent by isosceles triangles. The triangles are congruent by AAS, by cpctc the diagonals bisect.
yes, a pair of opposite sides is parallel and congruent
yes, opposite sides are congruent
yes, opposite angles are congruent
10. Yes alt. interior angle converse, no

4. Find all possible coordinates of vertex D of parallelogram ABCD.

5. Ch. 6.3: Proving Quadrilaterals are Parallelograms
Students will justify that a quadrilateral is a parallelogram

6. Given: Prove: ABCD is a parallelogram.

7. Theorem 6.6
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.7
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.8
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.
Theorem 6.9
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

8. Given: Prove: ABCD is a parallelogram.

9. Theorem 6.10
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram.

10. Practice Problems
Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies. 2. A B D C
1100
700 D C B A 12 8 9 C B A D
1. Yes, opp. Sides congruent 2. Yes AAS, DC is congruent to AB by CPCTC, one set of congruent and parallel sides 3. Yes, consecutive angles are supp,l

11. Let’s Review Ways to Prove a Shape is a Parallelogram:
Show that both pairs of opposite sides are parallel
Show that both pairs of opposite sides are congruent
Show that both pairs of opposite angles are congruent
Show that one angle is supplementary to both consecutive angles
Show that the diagonals bisect each other
Show that one pair of opposite sides are congruent and parallel

12. Quiz tomorrow on