Bell Work 3/6/13 1) Draw a pentagon that is: A) ConvexB) 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, If a quadrilateral is a parallelogram then its:

Theorems about Parallelograms(6.4) supplementary So, P + S = 180 Q + R = 180 and P + Q = 180 S + 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. Then look at the angles. A B CD 105 =105 = 75

Examples 4x – 9 = 3x + 18 x = 27 What do we know about opposite angles in a parallelogram?

Theorem the quadrilateral is a parallelogram

6.3 Notes the quadrilateral is a parallelogram

6.3 Notes the quadrilateral is a parallelogram = = 180

6.3 Notes the quadrilateral is a parallelogram

6.3 Proofs ∆PQT ∆RSTGiven CPCTC PT = RT and ST = QT PQRS is a parallelogram Diagonals bisect each other in a quadrilateral

6.3 Notes The quadrilateral is a parallelogram

6.3 Proofs If we mark what we know, how does that help us? What do we have to prove first? That the triangles are congruent Angle SQR is congruent to Angle PSQ because they are alternate interior angles. Both triangles share QS so it is congruent to itself. The triangles are congruent by SAS. PQ is congruent to RS. Both pairs of opposite are congruent, therefore PQRS is a parallelogram. How can we do that?

6.3 Rundown parallel 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

White Board Problems Find the value of the angles

White Board Problems Find the measure of missing angles

White Board Problems Find the value of the variables

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