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Warm Up

Warm Up. Determine if each quadrilateral must be a parallelogram. Tell me why . 1. . 2. . 3. . 4. . Warm Up. Determine if each quadrilateral is a parallelogram. Explain. . HW Check . P 315- 316 #2-18 even, #21-30 67 124 118 22; 18.5, 23.6, 23.6 18 m<Q = m<S = m<P = m<R = 144

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Warm Up

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  1. Warm Up Determine if each quadrilateral must be a parallelogram. Tell me why. 1. 2. 3. 4.

  2. Warm Up Determine if each quadrilateral is a parallelogram. Explain.

  3. HW Check P 315- 316 #2-18 even, #21-30 • 67 • 124 • 118 • 22; 18.5, 23.6, 23.6 • 18 • m<Q = m<S = m<P = m<R = 144 • X = 6, y =8 • X = 7, y= 10 • X = 3, y=4 • 3 • 3 • 6 • 6 • 9 • 2.25 • 2.25 • 4.5 • 4.5 • 6.75 P 324 #1-9, 12, 18 • 5 • X =3, y=4 • X =1.6, y=1 • 5/3 • 5 • 13 • Yes, both pairs of opposite sides are congruent • No, the quad. Could be a kite • Yes, both pairs of opp angles are congruent • a. Dist prop. b. Division property of equality c. AD//BC and AB//DC d. Converse of SSIA Thm e. Def of parallelogram 18. D

  4. Properties of Special Parallelograms

  5. Properties of Rectangles If: a quadrilateral is a rectangle Then: it is a parallelogram. If … B C A D … Then ABCD is a parallelogram

  6. Properties of Rectangles If: a parallelogram is a rectangle Then: then its diagonals are congruent. If … B C A D … Then AC BD

  7. Examples • A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM. • The rectangular gate has diagonal braces. Find HJ and HK. H K H L J J G M K 30.8 in L 48 in

  8. Properties of Rhombuses If: a quadrilateral is a rhombus Then: it is a parallelogram. If … B C A D … Then ABCD is a parallelogram.

  9. Properties of Rhombuses If: a parallelogram is a rhombus Then: its diagonals are perpendicular. B C If … A D … Then AC BD

  10. Properties of Rhombuses If: a parallelogram is a rhombus Then: each diagonal bisects a pair of opposite angles. 2 3 1 4 If … … Then <1 <2 <3 <4 <5 <6 <7 <8 B C 8 5 6 7 A D

  11. Examples D • CDFG is a rhombus. Find the measure of CD and m<GCH if m<GCD = (b+3)° and m<CDF = (6b – 40)°. • TVWX is a rhombus. Find each measure. C F H 5a 3a+17 G (5a-5)° 3b+4 x T Z (14a+20)° w V 13b-9

  12. Conditions Needed for a Rectangle If: the diagonals of a parallelogram are congruent Then: the parallelogram is a rectangle. C B If … A D AC BD … Then ABCD is a Rectangle

  13. Conditions Needed for a Rhombus If: diagonals of a parallelogram are perpendicular Then: the parallelogram is a rhombus. F G If … E H … Then ABCD is a rhombus.

  14. Conditions Needed for a Rhombus If: one diagonal of a parallelogram bisects a pair of opposite angles Then: the parallelogram is a rhombus. F G If … E H … Then EFGH is a rhombus.

  15. Tell whether each quadrilateral is a parallelogram, rectangle, rhombus, or square. (not drawn to scale) Give all the names that apply. 1. 2. 3.

  16. Whiteboard One Workbook for each pair Whiteboard for each person Practice 6-4: Complete the following questions:

  17. Quiz

  18. HW • P 332 #1-10, 16-18 • P 335 #66 – 75 (review)

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