Bell Work 3/6/13 1) Draw a pentagon that is: A) ConvexB) Concave 2) Find the value of x in the...

Bell Work 3/6/13

• 1) Draw a pentagon that is:• A) Convex B) Concave

• 2) Find the value of x in the quadrilaterals below. Is it regular? Why/Why not?

• A) B)

• ***The tablet password is: quadrilateral

Outcomes

• I will be able to:

• 1) Understand theorems about parallelograms

• 2)Find missing values of side lengths and angles in parallelograms

• 3) Prove that a quadrilateral is a parallelogram

Quadrilateral Investigation

• On the back of your bell work, use Geometry Pad to draw the quadrilateral ABDC and answer the questions.

• ***Change point C to (8, 5)• If you do not have your tablet, you may work with a partner, but you must answer the questions on your own paper.

• Turn in when finished, you have 15 minutes to complete this activity.

Results• What did you find about the slopes of

opposite lines in the quadrilateral?• They were the same, making the lines parallel.

So this figure was a parallelogram• What did you find about opposite angles?• They were congruent• What did you find about opposite side

lengths?• They were congruent

Parallelograms• Parallelogram: A quadrilateral with both pairs

of opposite sides parallel

• ***Arrows must be present to indicate that the lines are parallel

Theorems about parallelograms(6.2)• If a quadrilateral is a parallelogram then its:

Congruent

So, PS congruent to QR and PQ congruent to SR

Theorems about Parallelograms(6.3)

Congruent

So, QS

RP

and

If a quadrilateral is a parallelogram then its:

Theorems about Parallelograms(6.4)

supplementary

So, P + S = 180 Q + R = 180

and P + Q = 180S + R = 180

If a quadrilateral is a parallelogram then its:

Theorems about Parallelograms(6.5)

bisect each other

PM congruent to MR

and

SM congruent to MQ

If a quadrilateral is a parallelogram then its:

Examples

= 8

= 6

Examples

***Hint: It might help drawing a quadrilateral. Thenlook at the angles.

AB

CD

105

=105 = 75

Examples

4x – 9 = 3x + 18

x = 27

What do we know about oppositeangles in a parallelogram?

Theorem

the quadrilateral is a parallelogram

6.3 Notes

the quadrilateral is a parallelogram

6.3 Notes

120

60

60

the quadrilateral is a parallelogram

60 + 120 = 180

120 + 60 = 180

6.3 Notes

the quadrilateral is a parallelogram

6.3 Proofs

∆PQT ∆RST Given

CPCTC

PT = RT and ST = QT

PQRS is aparallelogram

Diagonals bisect each other in a quadrilateral

6.3 Notes

The quadrilateral is a parallelogram

6.3 Proofs

If we mark what we know, howdoes that help us?

What do we have to prove first? That the triangles are congruent

Angle SQR is congruent to Angle PSQbecause they are alternate interior angles. Both triangles share QS so it is congruent toitself. The triangles are congruent by SAS.PQ is congruent to RS. Both pairs of opposite are congruent, therefore PQRS is aparallelogram.

How can we do that?

6.3 Rundown

parallel

congruent

congruent

supplementary

bisect each other

congruent and parallel to each other

Exit Quiz• 1) Using what we know about quadrilaterals

find the value of x

• 2) Using what we know about parallelograms, find the value of x, y, and z

White Board Problem• Find the measure of the angles in each parallelogram

703

1102

701

White Board Problems

• Find the value of the angles

1003

802

1001

White Board Problems

• Find the measure of missing angles

503

152

1151

White Board Problems

• Find the value of the variables

324

1083

722

611

White Board Problems

• Find the length of TI in each of the following

• TI = 16

White Board Problems

• Find the length of TI

• TI = 22

White Board Problems

• Find the value of TI

• TI = 26

White Board Problems

• Find the value of TI

• GT = 8 and IE = 8

• TI = 4

6.3 Notes

the quadrilateral is a parallelogram