Happy Tuesday 

1. Happy Tuesday  Please take out the following: • Notebooks • Whiteboard and Whiteboard Pen • Homework Assignment List • Pg. 412 #1-9, 24-31, 33-35 Heads-Up: Unit 3 Test will be Friday

2. 6-4 Properties of Special Parallelograms Learning Objective: • Use properties of rectangles, rhombuses, and squaresto solve problems

3. 6-4 Properties of Special Parallelograms We are going to focus on three types of special quadrilaterals today. A rectangle, rhombus, and square. Using tick/arc marks, draw and label everything you know about rectangles on your whiteboards. Rectangle: • Quadrilateral with four right angles

4. 6-4 Properties of Special Parallelograms Properties of Rectangles: • If a quadrilateral is a rectangle, then it is a parallelogram. • If a parallelogram is a rectangle, then its diagonals are congruent. (AC ≅BD) Recall: What are the properties of a parallelogram?

5. Example 1 In rectangle CNRT, CN = 35 ft, and NT = 58 ft. Find each length. • TR (b) CE

6. Whiteboards A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. a) Find HM.

7. 6-4 Properties of Special Parallelograms Using tick/arc marks, draw and label everything you know about rhombuses on your whiteboards. Rhombus • Quadrilateral with four congruent sides

8. 6-4 Properties of Special Parallelograms Properties of Rhombuses: • If a quadrilateral is a rhombus, then it is a parallelogram. • If a parallelogram is a rhombus, then its diagonals are perpendicular. (AC ⊥ BD) • If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. Since this is a parallelogram, what should I add to the diagram?

9. Example 2: TVWX is a rhombus. • Find TV. • mVTZ.

10. Whiteboards CDFG is a rhombus. a) Find CD. b) mGCH if mGCD = (b + 3)° and mCDF = (6b – 40)°

11. 6-4 Properties of Special Parallelograms Using tick/arc marks, draw and label everything you know about squares on your whiteboards. Square • Quadrilateral with four right angles and four congruent sides

12. 6-4 Properties of Special Parallelograms Properties of Squares: • A quadrilateral with four right angles and four right sides.

13. 6-4 Properties of Special Parallelograms Do you consider a square to be a parallelogram? Write yes or no on your whiteboards. Be prepared to share your reasoning. Do you think a square is a rhombus? Write yes or no on your whiteboards. Be prepared to share your reasoning. Do you think a square is a rectangle? Write yes or no on your whiteboards. Be prepared to share your reasoning.

14. A square has all the properties of a rectangleand a rhombus.

15. Whiteboards PQRSis a rhombus. Find each measure. • QP • mQRP

16. Whiteboards The rectangular gate has diagonal braces. • Find HJ. • Find HK

17. Whiteboards Fill in the blank: If a parallelogram is a rhombus, then its diagonals are ___. If a parallelogram is a rectangle, then its diagonals are ___. If a quadrilateral is a rectangle, then it is a _____________. If a parallelogram is a rhombus, then each diagonal ______ a pair of opposite angles. If a quadrilateral is a rhombus, then it is a_____________.

18. 6-4 Properties of Special Parallelograms Try Example 3. If you need help, talk to your neighbors first, then ask me. Example 3

19. 6-4 Properties of Special Parallelograms Try Example 4. If you need help, talk to your neighbors first, then ask me. Example 4 Given: PQTS is a rhombus with diagonal Prove:

20. 15 Second Share Take 15 seconds to share with the person behind you something NEW you learned today. Take 15 seconds to share with the person diagonal to you something NEW you learned today. BE READY TO SHARE OUT!