Warm Up Determine if each quadrilateral must be

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

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

HW Check P 315 - 316 #2 -18 even, #21 -30 2. 67 4. 124 6. 118 8. 22; 18. 5, 23. 6 10. 18 12. m<Q = m<S = m<P = m<R = 144 14. X = 6, y =8 16. X = 7, y= 10 18. X = 3, y=4 21. 3 22. 3 23. 6 24. 6 25. 26. 27. 28. 29. 30. 9 2. 25 4. 5 6. 75 P 324 #1 -9, 12, 18 1. 5 2. X =3, y=4 3. X =1. 6, y=1 4. 5/3 5. 5 6. 13 7. Yes, both pairs of 8. 9. 12. 18. 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 D

Properties of Special Parallelograms

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

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

Examples 1. A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 K L cm. Find HM. H J M 2. The rectangular gate has diagonal braces. Find HJ and HK. H J 0. 8 L 3 G 48 in in K

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

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

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

Examples 1. CDFG is a rhombus. Find the measure of CD and m<GCH if m<GCD = (b+3)° and m<CDF = D (6 b – 40)°. C F H 5 a G 3 a+17 2. TVWX is a rhombus. Find each measure. 3 b+4 x (5 a-5)° T Z (14 a+20)° w 13 b-9 V

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

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

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

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

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

Quiz

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