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)

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

Find all possible coordinates of vertex D of parallelogram ABCD.

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

Given: Prove: ABCD is a parallelogram.

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.

Given: Prove: ABCD is a parallelogram.

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

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. 1. 3. 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

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

Quiz tomorrow on 6.1-6.3