Parallelogram with Vertices

​6.2 - Parallelograms

like when your grandmothers are standing next to each other​

​Parallelogram

→​ quadrilateral with both pairs of opposite sides parallel

​that's all we know... anything else is a theorem (raise the proof)

​Parallelogram Properties

​Parallelogram Diagonal Properties

Multiple Choice

Find the measure of the angle indicated in the following parallelogram.

• 95

• 90

• 81

• 86

Multiple Choice

Find the measure of the angle indicated in the following parallelogram.

• 105

• 46

• 112

• 40

Multiple Choice

Find the measure of the angle indicated in the following parallelogram.

• 97

• 105

• 95

• 45

Multiple Choice

Find the measure of the angle indicated in the following parallelogram.

• 150

• 108

• 65

• 55

Multiple Choice

Find the measure of the side indicated in the following parallelogram.

• 13

• 17

• 8

• 22

Multiple Choice

Find the measure of the side indicated in the following parallelogram.

• 23

• 8

• 24

• 18

Multiple Choice

• 1=30 ,  2=82,  3=50
• 1=32,  2=98 , 3=50
• 1=30 ,  2=98 , 3=50
• 1=30 , 2=98 , 3=40

Multiple Choice

• x = 9, y = 4

• x = 6, y = 4

• x = 6, y = 2

• x = 4, y = 2

Fill in the Blanks

Given the points of parallelogram ABCD, find where the diagonals intersect.

A (2, 1)

B (5, 6)

C (8, 2)

D (11, 7)

Fill in the Blanks

Given 3 points of parallelogram ABCD, find point D.

A (-3, -2)

B (-1, 5)

C (4, 7)

Fill in the Blanks

Given 3 points of parallelogram ABCD, find point D.

A (-3, -2)

B (4, 7)

C (-1, 5)

Fill in the Blanks

Given 3 points of parallelogram ABCD, find point D.

A (4, 7)

B (-3, -2)

C (-1, 5)

​6.3 - Tests for Parallelograms

Oh, it's a parallelogram? You think so? PROVE IT 😈

​Conditions for Parallelograms

Kind of like when we proved lines parallel

Multiple Choice

Is there enough information to determine that this quadrilateral is a parallelogram?

• yes, all opposite sides are congruent

• yes, opposite angles are congruent

• yes, opposite sides are parallel

• yes, consecutive interior angles are supplementary

Multiple Choice

State which method we can use to show that the quadrilateral is a parallelogram. 

• Both pairs of opposite angles are congruent.

• Both pairs of opposite sides are congruent.

• Both pairs of diagonals bisect each other.

• Both pairs of opposite sides are parallel. 

Multiple Choice

Is there enough information to determine that this quadrilateral is a parallelogram?

• yes, opposite sides are congruent

• yes, opposite sides are parallel

• no, not all pairs of opposite sides are congruent

• no, it is not a quadrilateral

Multiple Choice

State which method we can use to show that the quadrilateral is a parallelogram.

• Both pairs of opposite angles are congruent.

• Both pairs of opposite sides are congruent.

• The diagonals bisect each other.

• Both pairs of opposite sides are parallel.

Multiple Choice

Polygon ABCD is a Quadrilateral which of the following pieces of information would prove that ABCD is a parallelogram?

• DB=AC

• DA=BC

• DA||BC

• DA||BC, DA=BC

Multiple Choice

Is the quadrilateral a parallelogram?

• Yes; one pair of opposite sides are parallel

• Yes; one pair of opposite sides are congruent

• Yes; one pair of opposite sides are parallel and congruent

• No; only one pair of sides are parallel

• No; only one pair of sides are congruent

Multiple Choice

If you can prove that one pair of opposite sides of a parallelogram are the same length and have the same slope, you can prove that it is a parallelogram.

• Always

• Sometimes

• Never

Multiple Choice

Which theorem shows that the quadrilateral is a parallelogram?

• Parallelogram Diagonals Converse

• Parallelogram Opposite Sides Converse

• Parallelogram Opposite Angles Converse

• Opposite Sides Parallel and Congruent Theorem

Multiple Choice

Which theorem shows that the quadrilateral is a parallelogram?

• Parallelogram Diagonals Converse

• Parallelogram Opposite Sides Converse

• Parallelogram Opposite Angles Converse

• Opposite Sides Parallel and Congruent Theorem

Multiple Choice

Which theorem shows that the quadrilateral is a parallelogram?

• Parallelogram Diagonals Converse

• Parallelogram Opposite Sides Converse

• Parallelogram Opposite Angles Converse

• Opposite Sides Parallel and Congruent Theorem

Multiple Choice

Find the values of x and y that make the quadrilateral a parallelogram.

• x = 3, y = 2

• x = 25, y = 15

• x = 15, y = 25

• x = 113, y = 67

Multiple Choice

Find the values of x and y that make the quadrilateral a parallelogram.

• x = 4, y = 3

• x = 3, y = -2

• x = 1, y = 4

• x = 3, y = 4

Multiple Choice

Find the value of x that makes the quadrilateral a parallelogram.

• x = -4

• x = 1

• x = 8

• x = 34

Multiple Choice

Find the value of x that makes the quadrilateral a parallelogram.

• x = 26

• x = 7

• x = 2

• x = -2

Multiple Choice

Given the points for quadrilateral ABCD, determine if it is a paralleogram.

A (-2, -4)

B (2, -7)

C (8, 3)

D (4, 6)

• yes

• no

• not enough information

• maybe

Multiple Choice

Given the points for quadrilateral ABCD, determine if it is a paralleogram.

A (6, 7)

B (-2, 5)

C (-7, 8)

D (1, 11)

• yes

• no

• not enough information

• maybe

Fill in the Blanks

Given 2 points from parallelogram ABCD and the intersection point E of the diagonals, find point C.

A (-8, 2)

B (-3, -4)

E (-3, 3)

Fill in the Blanks

Given 2 points from parallelogram ABCD and the intersection point E of the diagonals, find point D.

A (-8, 2)

B (-3, -4)

E (-3, 3)