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Geometry Lesson: Parallelograms & Proofs

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Welcome back! Today's lesson focuses on parallelograms in the coordinate plane. Remember to pick up papers, take out notes, and be prepared for whiteboard activities. Homework includes pg. 402, #1-8, 26-27 and more. Don't forget, extra credit and upcoming tests. Let's dive into properties and proofs of parallelograms.

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Geometry Lesson: Parallelograms & Proofs

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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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