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

A D

C

2.3.

(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

A D

C(180 – x)o

(180 – x)oxo

xo

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

A D

C(180 – x)o

(180 – x)oxo

xo

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 perpendicularbisectors of eachother.A (-1, 0)B (-3, 5)C (2, 7)D (4, 2)