Parallelograms. Lesson 6-l. AB=CDandBc=AD. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other but are not congruent
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1 Lesson 6-l Parallelograms Lesson 6-'1 : Parallelogram N" 1. Both pairs of opposite sides are congruent. AB=CDandBc=AD 2. Both pairs of opposite angles are congruent. /.A = Z.C and /.8 = /-D 3. Consecutive angles are supplementary. m/-a + mzb - 180' ctnd mz.a + mld - 180" m/.8 + m/.c = 180" and m/.c * m/.d = 180' 4. Diagonals bisect each other but are not congruent P is the midpoint of AC and, BD. AP = PC -HP = PD Lesson 6-1 : Parallelogram
2 Parallelogram Definition: A quadrilateral whose opposite sides are parallel. Z,lilcr: ananclfo B Symbol: Naming: o a a smaller version of a parallelogram A parallelogram is named using all four vertices. You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction. For example, the figure above can be either Dtgco or Dtocs. Lesson 6-1 : Parallelogram 2 Exampfles HK: and HP : 3. m<k: m( 4. m<l * m( : : 180o. 5. If m<p : 65o, then m<h : : and m<l 6. Draw the diagonals with their point of intersection labeled M. 7. -,rrr{k If HM: 5, then ML : ;s _ 8. If KM :'7, then KP : - ar g. If HL : 15, then ML : units. 0. If m<hpk:36o, then m<pkl :. (Alternate interior angles are congruent.. Lesson 6-1 ; Parallelogram
3 b-l Chapter 6: Quadrilaterals Lesson 6-1: Parailelograms Classwork Name Comolete each statement. 1. In a parallelogram, opposite angles are 2. In a parallelogram, opposite sides are and 3. In a parallelogram, consecutive angles are 4. How many sides does every parailelogram have? 5. Are the diagonals congruent in a parallelogram?. 6. In parallelogram ABCD, AB = 7. In parallelogram ABCD, <B is consecutive to < and < 8. In parallelogram ABCD, if m<c = 47", then m<a E _, and m<d = _ 9. In paratlelogram ABCD if the diagonals intersect at P, then AP = BP= i0. In parallelogram ABCD, TD ll m<b = and ABCD is a parallelo-eram. State the reason that justifies each statement. 11. <DAB = <DCB 12. -BE= ED 13. AD =-BC 14. <DAB and <ABC are supplementary rs TDllEe 16. <3 - <2 A Complete each statement. using the diagram from # If AD = 20, BC = 18. If m<adc = 115', then m<abc = 19. If DB = 22,then DE = 20. If AE = 18, then AC = 21. If m<dab =75o, m(adc = 23. lf m<aed ='72", m<dec = 22. It m<1 = 30", then m<4 = 24. If m<adc = 130" and m<l = 35", m<2 = - 3
4 Lesson : Parallelogram Integrated III Name Find the missin=s measurements of Parallelogram ABCD. AB=4 BC=16 CD= DA= AC=14 DB=18 AE= BE= CE= DE= m<abe = 38" m<ebc = 24" m<bce = 30" m<cde = m<eda = m<dae = rn<aeb = m<bec = m<ced = m<ecd = m<eab = m<dea = Find the missing measurements of Palallelogram ABCD. AB=10 BC=24 CD= A DA= AC= DB= AE=12 BE=13 CE= DE= m<abe = 47' m<ebc = 27" m<bce = m<cde = m<eda = m<dae = r-n(aeb = m<bec = m<ced = n<ecd = 72" m<eab = m<dea = 4
5 Chapter 6: Quadrilaterals Lesson 6-1,: Parallelograms Homework Name Use the diasram of the oarallelosram to the risht to answer the followins ouestions. 1. If m<mpo = 122", then m<pon = _. 2. If m<pmn = 74', then m<nop = 3. If m<4 = 36", then m< =36' If m<mno = 106' and m<4 = 47", thenm<33_,. 5. IfNR = 3x + 2 andrp = x + 14, then x=_,nr= andnp=_ 6. If MR = 2x + 4 andmo = 7x - 28, then x=-,ro= and MO =. M 7. If m<pmn = 8x - 5 and m<pon = 4x + 19, then x = _, m<pmn = _ and m<mno = _ 8. If m<mpo = 9x + 2 and m<pon = 5x + 10, then x = _, m<mpo r _, m<pon r _, and m<pmn = _. Comnlete each statement usins oarallelosram KLMN. 9. IfKN = 3x - 5 andlm = x + 9, then KN = x 10. If KL=: andmn=2x-9, 2 thenkl=_. i1. Ifm(L = 4x + 11 and m<k = 6x - then m<k = t, 12. Ifm<L = x + 40 and m<n = 3x - 6, then m<l = 5
6 Find the values of x. y and z if each quadrilateral is a parallelogram. 13. t4. 96" x= y= z= x= y= z= 15. x- y= Z: 16. In parallelogramwxyz, if m<w = 3p and m<x = 4p + 33, find p and the measure of all four angles. Explain whv it is impossible for each fisure to be a oarallelosram " ' 1.2s" 19. Quad TRAP has verlice st(-2,-1), R(2, 3), A(7,3), and P(3, -1). Is TRAP also a palallelogram? Explain why or why not? b
7 Multiple Choice Identify the choice that best cornpletes the statement or answers the qttestion. f-----;l 1. lr ABCD is a parallelogram,,nae =15, and,nde = 9. What is the measure of BD? AB A9 815 c18 D30 f= '' nurois a parallelogram,,{b = B, una E = g. what is the measure of BC? A$e A5 B8 c10 D16 i--*-f 3 ABCD is a paralellogram ur6m[c = 21. x? 11*r-arr- =?-r, then what is the value of A6 B3 c14 D28
8 [-l lr 4. ABCD is a paralellogram. Which of the following pairs of angles are not necessarily congruent? A B C D LADI:, L,4B{: /.DEA, I&48 L4EB, ICED LABE, /ED( Use the figure below to answer the next 2 questions. AR n f.r f---; tt f---i 5. Which of the following must be true of parallelogram PQRS? A QT: TR B PT: TR C PQ= RQ D Pft=85 6. Which of the following must be true of parallelogram PQRS? A /.t2er = /RCF B /TPS = /TPS C /.!P[i = ^{PSR D ttpr= ttsr
9 6-1 Warmup Numeric Response ABCD is a parallelogram. A Use this figure to answer the questions below. '',re = I 8, u,hatie B-C? 2' y,+c= 10,whatis AE? I 3' r*/.aec = 82", flr,lii+/.dac, ml.dti?rrtc) rn/.f,dc, reepectr,reiy. If 4',ffi:5y+ 11 ;rrtdile=ly+l1,rl,'hatis ED? If 5. m/!l = 15"and rnle:48", finrj m/.,48c. If 1
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