Warm Up:  Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving?  What is the measure of CD? 

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Warm Up:  Solve for x and y in the following parallelogram. What properties of parallelograms did you use when solving?  What is the measure of CD?  What is the measure of Angle C?  What is the sum of the interior angles of a dodecagon? 1. B AD C (16x – 4) o (14x + 34) o 2y + 85y – 1 4.

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its opposite sides are congruent.

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its opposite sides are congruent.  IF both pairs of opposite sides of a quadrilateral are congruent, THEN the quadrilateral is a parallelogram.

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its opposite angles are congruent.

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its opposite angles are congruent.  IF both pairs of opposite angles of a quadrilateral are congruent, THEN the quadrilateral is a parallelogram.

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its consecutive angles are supplementary. B AD C (180 – x) o xoxo xoxo

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its consecutive angles are supplementary.  IF an angle of a quadrilateral is supplementary to both of its consecutive angles, THEN the quadrilateral is a parallelogram. B AD C (180 – x) o xoxo xoxo

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its diagonals bisect each other.

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF a quadrilateral is a parallelogram, THEN its diagonals bisect each other.  IF the diagonals of a quadrilateral bisect each other, THEN the quadrilateral is a parallelogram.

Conditions of Parallelograms (6.3) and Special Parallelograms (6.4)  IF one pair of opposite sides of a quadrilateral are parallel AND congruent, THEN the quadrilateral is a parallelogram.

Show that ABCD is a parallelogram for m = 12 and n = 9.5; which one of the conditions of parallelograms did you use? B A D C (2m + 31) o (12n + 11) o (7m – 29) o

Are each of the given quadrilaterals also parallelograms? Justify your answer. # 1 # 2 # 3 7 7

Find x and y so the quadrilateral is a parallelogram. B A D C (4x – 8) o (1/2 y) o (3y – 4) o (x – 12) o

RECTANGLES

RECTANGLE  Four Right Angles  Congruent Diagonals  Properties of a Parallelogram

RHOMBUSES

RHOMBUS  Four Congruent Sides  Perpendicular Diagonals  Diagonals Bisect Opposite Angles  Properties of a Parallelogram

SQUARES

SQUARE  Properties of a Rectangle  Properties of a Rhombus

ABCD is a rhombus. Find the measure of Angle B. B A D (2y + 10) o (y + 2) o C

Show the diagonals of square ABCD are congruent perpendicular bisectors of each other. A (-1, 0) B (-3, 5) C (2, 7) D (4, 2)