LAP 1 TOOLS OF GEOMETRY VOCABULARY, THEOREMS AND POSTULATES

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1 Point - LAP 1 TOOLS OF GEOMETRY VOCABULARY, THEOREMS AND POSTULATES Line - Plane - Collinear Points - Coplanar- Segment- Ray-

2 Opposite Rays- LAP 1 TOOLS OF GEOMETRY Postulate or Axiom- POSTULATE 1-1- POSTULATE 1-2- POSTULATE 1-3- POSTULATE 1-4-

3 RULER POSTULATE- LAP 1 TOOLS OF GEOMETRY SEGMENT ADDITION POSTULATE- Congruent Segments - Midpoint-

4 Segment Bisector (bisects)- LAP 1 TOOLS OF GEOMETRY Angle - PROTRACTOR POSTULATE- ANGLE ADDITION POSTULATE

5 Types of Angles- LAP 1 TOOLS OF GEOMETRY Congruent Angles- Adjacent angles- Vertical Angles-

6 Complementary angles- LAP 1 TOOLS OF GEOMETRY Supplementary Angles- Linear Pair- LINEAR PAIR POSTULATE-

7 Angle Bisector (bisects)- LAP 1 TOOLS OF GEOMETRY Perpendicular Lines- Perpendicular Bisector (bisects)- MIDPOINT FORMULA- Diagram: Coordinate Plane:

8 DISTANCE FORMULA- LAP 1 TOOLS OF GEOMETRY Perimeter- Area- AREA ADDITION POSTULATE-

9 Name Date Class SECTION 1-2 POINTS, LINES AND PLANES Geometry is a mathematical system built on accepted facts, basic terms, and definitions. In Geometry, we have undefined terms: point, line, plane. Undefined terms are the basic ideas that you can use to build definitions of ALL other figures in geometry. Although you cannot define them, it is important to have a general description of their meanings. EX 1: Use the figure on the right to answer the questions. A. What are two other ways to name QT? B. What are two other ways to name plane P? C. What are the names of 3 collinear points? D. What are the names of 3 coplanar points? E. What are two points that are not coplanar to R, S, and V? EX 2: Use the figures below to answer the questions. It is the same figure for each questions. A. What are the names of the segments? B. What are the names of the rays? C. What are the opposite rays? D. EF and FE form a line, are they opposite rays?

10 Name Date Class EX 3: What is the intersection of plane ADC and plane BFG? What type of intersection should it be? EX 4: What is plane contains N, P, and Q? Shade the plane. EX 5: What is plane contains J, M, and Q? Shade the plane. EX 6: Determine whether each statement is always, sometimes, or never true. A. GH and HG are the same ray. B. JI and JL are opposite rays. C. A plane contains only three points. D. Three noncollinear points are contained in only one plane. E. If three points are coplanar, they are collinear.

11 Name Date Class SECTION 1-3 MEASURING SEGMENTS EX 1: What is ST? EX 2: What is UV? EX 3: What is SV? EX 4: If EG 59, EF 8x 14, and FG 4x 1, what are EF and FG? EX 5: If EG 4x 2, EF 10, and FG 2x 2, what are JK and KL? EX 6: Are AC and BD congruent? EX 7: What are the midpoint of PR? What are PQ, QR, and PR?

12 Name Date Class EX 1: What are two other names for 1? SECTION 1-4 MEASURING ANGLES EX 2: What are two other names for KML? EX 3: Would it be correct to name any of the angles M? EX 4: What are the measures of LKN, JKL, and JKN? Classify each angle. EX 5: If RQT 155, what are RQS and TQS? EX 6: What are DEC and CEF? EX 7: Your class concludes from the diagram that JKL LKM. Is your classmate correct? Explain.

13 Name Date Class SECTION 1-5 EXPLORING ANGLE PAIRS EX 1: Use the diagram. Is the statement true? Explain. A. BFD and CFD are adjacent angles. B. AFB and EFD are vertical angles. C. AFE and BFC are complementary. D. AFE and CFD are vertical angles. E. BFC and DFE are supplementary angles. EX 2: What can you conclude about the following diagrams? A. B. EX 3: KPL and JPL are a linear pair, KPL 2x 24 and JPL 4x 36. What are the measures of KPL and JPL? EX 4: bisects DAB. If DAC 58, what is DAB?

14 Name Date Class SECTION 1-6 BASIC CONSTRUTIONS EX 1: Draw the following situation and mark the drawing. A. bisects at point C. ACE ECB. What can you conclude about the drawing? B. bisects WXZ. What can you conclude about the drawing? EX 2: What can you concluding about the drawings? A. B. C. D. E.

15 Geometry B Name ID: 1 K r2n0\1m7k bkiuhtpas zsboifvtbwaayrcer rl\l\c^.c a OAslKl[ mrxijgjhgtksv Ur`e[sde[rEvxe^dl. Sec. 1.6 Worksheet Write if the statement given is indicated by the marks on the diagram. Date Period 1) 2) V Y X S T U W Q R T d c b YX XU SQ 3) E 4) A J F K D S P B U Q C T R EK QX h _2r0G1p7v qkhuvtrae ]SVoHfWtmwxaArheQ VLLL\Cf.k z OAFlIlV jrpiogbhztwsg QrOeNsdeSryvuedda.n L wmdahdset DwKiFtZhw CIgnffei_nniZtred DGKetormiejtgrEyw. -1- Worksheet by Kuta Software LLC

16 5) R 6) T Q W V S U T U P SR TU UW 7) 8) T C E U S L B D R K V CE BC W SV WV List all information given by the marks on the diagram. Make sure to name all figures (segments, lines, angles, etc.) with the CORRECT notation. 9) 10) A Q R B S T C D E F A n2r0g1s7l xkvupt_ad osnonfmtswmaqrjej vlllkce.j I ^AvlEl[ QrxijgUhvtisk krreos]eqrdvaejde.o H mmuandjei MwEiGtBhA oisntfei^nzictqei igteuoembeetsrryu. -2- Worksheet by Kuta Software LLC

17 11) 12) V S D F T X W C E U 13) Q P 14) U R R S U Q S T T 15) A 16) B M G F F L E D C E D n ]2Q0Y1O7o HKquZt\ay us[o^fntywra\reee ^LrLbCF.^ ] KAClylD prpingthttdsk urfebs]elrhvieod_._ i mmia_d`eb ]w\i]tghg LISntfaiEnoiztRew TGaeSoumGedtyrvyC. -3- Worksheet by Kuta Software LLC

18 17) f e d 18) T R Q S R S Q P 19) 20) E D B P S U Q C F T R 21) 22) D F D B C E C B E G l J2j0o1A7u tkcu[tyaj ASioCfMtDwZabrKeF BLmLWC].D ] caulwlu SrmivgmhvtIsd UrAehs\evrOvMefd^.G A omgapdnej wwuiztthf MImnFfEiDnaistxeY JGjeJotmIejtJr[yQ. -4- Worksheet by Kuta Software LLC

19 Answers to Sec. 1.6 Worksheet (ID: 1) 1) Not given by the diagram 2) Not given by the diagram 3) Given by the diagram 4) Not given by the diagram 5) Not given by the diagram 6) Given by the diagram 7) Given by the diagram 8) Not given by the diagram 9) TR SQ 10) EB DC 11) TU ST SU VW 12) DC FE CE DF 13) TS PQ 14) QS QR RST 15) EFD DFC AM 16) ED GF DF EG GF FD 17) f e QR d ST 18) PQ RS SQ RP SQ 19) QR PQ PR ST STU 20) BD BDC CDE 21) CD BC EF BD EFG 22) DE BC BC EC DB k X2Y0u1u7Y hkdumtoak LS\oKfFtIwDalrWek DLlLdCk.l O HAUlOls _ruifgwhptbsh HrBe`sVeJrrv[eadC.c B LMFaUd_en PwIiVt^hM xilnafviantivtxez ngsefotm_eet`rpyr. -5- Worksheet by Kuta Software LLC

20 Name Date Class SECTION 1-7 MIDPOINT AND DISTANCE FORMULAS EX 1: On a number line, has endpoints -3 and 7. What is AB? What is the coordinate of the midpoint? EX 2: has endpoints E(7, 5) and F(2, -4). What are the coordinates of its midpoint M? EX 3: The midpoint of is M(-2, 1). One endpoint is C(-5, 7). What are the coordinates of the endpoint D?

21 Name Date Class EX 3: What is the distance between U(-7, 5) and V(4, -3)? Round to the nearest tenth.

22 Geometry B Name ID: 1 V S2[0V1h7j nksust`az csqohfotbwhanrbex PLULgCP.^ A `AolPlM lrziogqhptgsy jrleesreoruvuetdu. Sec. 1.7 Worksheet Date Period Find the midpoint of the line segment with the given endpoints. Give answers in decimals. 1) (-8, -7), (1, -6) 2) (0, -5), (8, -4) 3) (3, 6), (-10, -7) 4) (-6, 7), (-5, -8) 5) (2, -10), (9, 9) 6) (2, 9), (-9, 0) Find the midpoint of each line segment. Give answers in decimals. PLOT and LABEL the midpoint with its ordered pair. 7) y 8) y x x ^ B2q0Q1M7W _KAuptPaL jsiosfftuwfanrjep SL`LWCW.g q IAvlRlg TrJiVg^hbtqsg TrdeJs\e_rxvqeCdX.l f OMcagdxep ZwNiwt\ha XIZnZfUiUnrivtCeH sg\esovmpeutqrcyp. -1- Worksheet by Kuta Software LLC

23 9) y 10) y x x ) y 12) y x x Find the other endpoint of the line segment with the given endpoint and midpoint. 13) Endpoint: (1, 6), midpoint: (-2, 3) 14) Endpoint: (10, 5), midpoint: (-6, -3) Find the distance between each pair of points. Give answer in decimals, round to the nearest tenth if necessary. 15) (2, 2), (3, -2) 16) (6, -6), (-2, 2) c l2p0e1m7h ZKkuVthas [S^oUfitQwUagr_ei TL]LtCi.K ^ aaklulm [rqifgqh`ttso drhepszeorsvoehdf.z X PMHaLdHeO NwIietrhd BIynffeiWn_igtOeM ngceyoumcegternyr. -2- Worksheet by Kuta Software LLC

24 17) (2, -6), (0, -5) 18) (7, -6), (6, 2) 19) y 20) y x x ) y 22) y x x o I2N0]1o7D dkmultfak ts^oyf[t\wvahreer glolrca.y J DADlflB srwi\grhptisv [rvessrevrevjewdn._ N PM^aTdGeb vwgictdhc hidnvfyiynfidtjep ggwemo^mfeytfrcyr. -3- Worksheet by Kuta Software LLC

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