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Welcome Back!

Welcome Back!. Pick up the pieces of paper on the front table Take out notes from Monday before break Take out your whiteboard and whiteboard marker Tonight’s Homework Pg. 402 #1-8, 26- 27; p 395: 14, 26, 44 Remember: Extra Credit is due tomorrow

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Welcome Back!

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  1. Welcome Back! • Pick up the pieces of paper on the front table • Take out notes from Monday before break • Take out your whiteboard and whiteboard marker Tonight’s Homework • Pg. 402 #1-8, 26-27; p 395: 14, 26, 44 Remember: • Extra Credit is due tomorrow • Periods 1 &3: FACEing Geometry due tomorrow Heads Up • Unit 3 Test on Monday( this is your last test in your 35% test category)

  2. 3 Things

  3. Example 3: Parallelograms in the Coordinate Plane Three vertices of JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of vertex M. Remember: When you are drawing a figure in the coordinate plane, the name gives the order of the vertices.

  4. Example 3: Parallelograms in the Coordinate Plane • Step 1: Graph the points. • Step 2: Find the slope of KL by counting the units from K to L. • Step 3: Start at J and count the same number of units. • Step 4: Use the slope formula to verify that

  5. Example 4: Properties of Parallelograms in a Proof Given: ABCD is a parallelogram. Prove:∆AEB∆CED

  6. 3.diags. bisect each other 2.opp. sides  Proof: 1. ABCD is a parallelogram 1. Given 4. SSS Steps 2, 3

  7. Whiteboards Justify why

  8. What do you remember…? Lets refresh. What are the properties of parallelograms? I am going to call on you randomly. Please be prepared and do not repeat what someone else says. Today we will be showing that specific quadrilaterals are parallelograms.

  9. 6-3 Conditions for Parallelograms Learning Objective: • Prove that a given quadrilateral is a parallelogram.

  10. 6-3 Conditions for Parallelograms

  11. 6-3 Conditions for Parallelograms

  12. Example 1: Verifying Figures are Parallelograms Show that JKLM is a parallelogram for a = 3 and b = 9.

  13. Whiteboards Show that PQRS is a parallelogram for x = 10 and y = 6.5.

  14. 6-3 Conditions for Parallelograms Example 3: (You Do) Show that PQRS is a parallelogram for a = 2.4 and b = 9.

  15. Example 3: Applying Conditions for Parallelograms Determine if the quadrilaterals must be a parallelogram. Justify your answer.

  16. Example 3: Applying Conditions for Parallelograms Determine if the quadrilaterals must be a parallelogram. Justify your answer.

  17. Example 3: Applying Conditions for Parallelograms Determine if the quadrilaterals must be a parallelogram. Justify your answer.

  18. Example 3: Applying Conditions for Parallelograms Determine if the quadrilaterals must be a parallelogram. Justify your answer.

  19. Example 4: Proving Parallelograms in the Coordinate Plane Show that quadrilateral JKLM is a parallelogram by using the definition of parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0).

  20. Math Joke of the Day! • Did you hear about the quadrilateral who wanted to be a parallelogram? Yes, his opposite angles weren’t quite up to par.

  21. Example 4: Application The legs of a keyboard tray are connected by a bolt at their midpoints, which allows the tray to be raised or lowered. Why is PQRS always a parallelogram?

  22. Whiteboards 1. Show that JKLM is a parallelogram for a = 4 and b = 5. 2. Determine if QWRT must be a parallelogram. Justify your answer. JN = LN = 22; KN = MN = 10; so JKLM is a parallelogram No; One pair of consecutive s are , and one pair of opposite sides are ||. The conditions for a parallelogram are not met.

  23. Whip Around We are going to share one thing we learned today. I will choose the first person to share, then you all will be responsible for choosing who will share next.

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