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

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

HW Check P #2-18 even, # ; 18.5, 23.6, m<Q = m<S = m<P = m<R = X = 6, y =8 16.X = 7, y= X = 3, y= P 324 #1-9, 12, X =3, y=4 3.X =1.6, y=1 4.5/ Yes, both pairs of opposite sides are congruent 8.No, the quad. Could be a kite 9.Yes, both pairs of opp angles are congruent 12.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

Properties of Special Parallelograms

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

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

Examples 1.A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM. 2.The rectangular gate has diagonal braces. Find HJ and HK. J KL M H G HJ K L 48 in 30.8 in

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

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

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

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

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

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

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

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

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

Quiz

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