Vocabulary - Weebly
4-1Congruent FiguresVocabularyReview1. Underline the correct word to complete the sentence.A polygon is a two-dimensional figure with two / three or more segments thatmeet exactly at their endpoints.2. Cross out the figure(s) that are NOT polygons.Vocabulary BuilderMain Idea: Congruent figures have the same size and shape.Related Word: congruence (noun)Use Your Vocabulary3. Circle the triangles that appear to be congruent.Write T for true or F for false.4. Congruent angles have different measures.5. A prism and its net are congruent figures.6. The corresponding sides of congruent figures have the same measure.Chapter 490Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.congruent (adjective) kahng GROO unt
Key Concept Congruent FiguresCongruent polygons have congruent corresponding parts—their matchingsides and angles. When you name congruent polygons, you must listcorresponding vertices in the same order.ABFEDCGHABCD EFGH7. Use the figures at the right to complete each congruence statement.AB BC CD DA /A /B /C /D Problem 1 Using Congruent PartsGot It? If kWYS O kMKV , what are the congruent corresponding parts?8. Use the diagram at the right.Draw an arrow from each vertex of thefirst triangle to the correspondingvertex of the second triangle.ȿW Y S ƹ ȿ M K V9. Use the diagram from Exercise 8 to complete each congruence statement.SidesWY YS WS Angles/W /Y /S Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.Problem 2 Finding Congruent PartsGot It? Suppose that kWYS O kMKV. If m/W 5 62 and m/Y 5 35,what is mlV ? Explain.YUse the congruent triangles at the right.í10. Use the given information to label thetriangles. Remember to write correspondingvertices in order.í11. Complete each congruence statement./W W/Y /S 12. Use the Triangle Angle-Sum theorem.m/S 1 m1m5 180, so m/S 5 180 2 (1), or.13. Complete.Since /S and m/S 5, m/V 5.91Lesson 4-1
Finding Congruent TrianglesProblem 3DGot It? Is kABD O kCBD? Justify your answer.14. Underline the correct word to complete the sentence.To prove two triangles congruent, show that all adjacent / correspondingparts are congruent.ACB15. Circle the name(s) for nACD.acuteisoscelesrightscalene16. Cross out the congruence statements that are NOT supported by the information inthe figure.AD CDBD BDAB CB/A /C/ABD /CBD/ADB /CDB17. You needcongruence statements to prove two triangles congruent, so youcan / cannot prove that nABD nCBD.Theorem 4–1 Third Angles TheoremTheoremIf . . .Then . . .If two angles of one triangleare congruent to two angles ofanother triangle, then the thirdangles are congruent./A /D and /B /E/C /FBCEFUse kABC and kDEF above.18. If m/A 5 74, then m/D 5.19. If m/B 5 44, then m/E 5.20. If m/C 5 62, then m/F 5.Problem 4Proving Triangles CongruentAGot It? Given: lA O lD, AE O DC,EB O CB, BA O BDBCDEProve: kAEB O kDCB21. You are given four pairs of congruent parts. Circle the additional information youneed to prove the triangles congruent.A third pairof congruentsidesChapter 4A second pairof congruentangles92A third pairof congruentanglesCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.DA
22. Complete the steps of the proof.1) AE , EB , BA 1) Given2) /A 2) Given3) /ABE 3) Vertical angles are congruent.4) /E 4) Third Angles Theorem5) nAEB 5) Definition of trianglesLesson Check Do you UNDERSTAND?If each angle in one triangle is congruent to its corresponding angle in anothertriangle, are the two triangles congruent? Explain.23. Underline the correct word to complete the sentence.To disprove a conjecture, you need one / two / many counterexample(s).Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.24. An equilateral triangle has three congruent sides and three 608angles. Circle theequilateral triangles below.25. Use your answers to Exercise 24 to answer the question.Math SuccessCheck off the vocabulary words that you understand.congruentpolygonsRate how well you can identify congruent polygons.Need toreview02468Now Iget it!1093Lesson 4-1
4-2Triangle Congruenceby SSS and SASVocabularyReviewA1. Use the diagram at the right. Find each.Bincluded angle between AB and CAincluded side between /A and /CCincluded angle between BC and CAincluded side between /B and /Cincluded angle between BC and ABincluded side between /B and /Apostulate (noun)PAHSchuh litDefinition: A postulate is a statement that is accepted as true without beingproven true.Main Idea: In geometry, you use what you know to be true to prove new things true.The statements that you accept as true without proof are called postulatesor axioms.Use Your Vocabulary2. Underline the correct word to complete the sentence.You can use properties, postulates, and previously proven theorems asreasons / statements in a proof.3. Multiple Choice What is a postulate?a convincing argument using deductive reasoninga conjecture or statement that you can prove truea statement accepted as true without being proven truea conclusion reached by using inductive reasoningChapter 494Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.Vocabulary Builder
Postulate 4–1 Side-Side-Side (SSS) PostulatePostulate 4-1 Side-Side-Side (SSS) PostulateIf the three sides of one triangle are congruent to the three sidesof another triangle, then the two triangles are congruent.4. Use the figures at the right to complete the sentence.If AB DE, BC EF, and AC , then nABC nBEAD.CFProblem 1 Using SSSCGot It? Given: BC O BF, CD O FDProve: kBCD O kBFDB5. You know two pairs of sides that are congruent. What else do youneed to prove the triangles congruent by SSS?DF6. The triangles share side.Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.7. Complete the steps of the proof.StatementReason1) BC 1) Given2) CD 2) Given3) BD 3) Reflexive Property of 4) nBCD 4) SSSPostulate 4–2 Side-Angle-Side (SAS) PostulatePostulate 4–2 Side-Angle-Side (SAS) PostulateIf two sides and the included angle of one triangle are congruent to two sides and theincluded angle of another triangle, then the two triangles are congruent.Use the figures below to complete each statement.BSETA8. nDEF by SAS.9. nABC by SSS.C DF95RLesson 4-2
Problem 2 Using SASGot It? What other information do you need to proveLENBkLEB O kBNL by SAS?10. Circle the angles that are marked congruent in the diagram./EBL/ELB/NBL/NLB11. Circle the sides that form the angles that are marked congruent in the diagram.BEBLBNLBLELN12. Complete each congruence statements.LB /BLE Underline the correct word(s) to complete each sentence.13. Proving nLEB nBNL by SAS requires one / two pair(s) of congruent sides andone / two pair(s) of congruent angles.14. The diagram shows congruency of zero / one / two pair(s) of congruent sides andzero / one / two pair(s) of congruent angles.15. To prove the triangles congruent by SAS, you still need zero / one / two pair(s) ofcongruent sides and zero / one / two pair(s) of congruent angles .16. To prove the triangles congruent, you need to proveandcongruent.Got It? Would you use SSS or SAS to prove the triangles below congruent? Explain.Complete each statement with SSS or SAS.17. Use 9 if you have three pairs of sides congruent.18. Use 9 if you have two pairs of sides and the included angle congruent.Write T for true or F for false.19. The diagram shows congruence of three sides.20. In the triangle on the left, the marked angle is the included angle of the sidewith two marks and the side with three marks.21. In the triangle on the right, the marked angle is the included angle of the sidewith two marks and the side with three marks.Chapter 496Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.Problem 3 Identifying Congruent Triangles
22. Would you use SSS or SAS to prove the triangles congruent? Explain.Lesson Check Do you UNDERSTAND?Error Analysis Your friend thinks that the triangles below are congruent by SAS.Is your friend correct? Explain.23. Are two pairs of corresponding sides congruent?Yes / No24. Is there a pair of congruent angles?Yes / No25. Are the congruent angles the included angles between thecorresponding congruent sides?Yes / NoCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.26. Are the triangles congruent by SAS? Explain.Math SuccessCheck off the vocabulary words that you understand.congruentcorrespondingRate how well you can use SSS and SAS to prove triangles congruent.Need toreview02468Now Iget it!1097Lesson 4-2
4-3Triangle Congruenceby ASA and AASVocabularyReview1. Cross out the figure(s) that are NOT triangle(s).2. A triangle is a polygon withsides.3. A triangle with a right angle is called a(n)obtuse / right / scalene triangle.Vocabulary Buildercorresponding sidesAXOther Word Forms: correspond (verb); correspondence(noun)Definition: Corresponding means similar in position,purpose, or form.C YBZMath Usage: Congruent figures have congruentcorresponding parts.Use Your VocabularyDraw a line from each part of kABC in Column A to the corresponding part ofkXYZ in Column B.Column AColumn B4. BC/Z5. /A/Y6. ABYZ7. /C/X8. ACXY9. /BXZChapter 498BAYCZXCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.corresponding (adjective) kawr uh SPAHN ding
Postulate 4–3 Angle-Side-Angle (ASA) PostulatePostulateIf . . .Then . . .If two angles and the includedside of one triangle arecongruent to two angles andthe included side of anothertriangle, then the two trianglesare congruent./A /D, AC DF, /C /FnABC nDEFBAECDF10. Explain how the ASA Postulate is different from the SAS Postulate.Problem 1 Using ASAGot It? Which two triangles are congruent by ASA? Explain.HCFONCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.GAIT11. Name the triangles. List the vertices in corresponding order: list the vertex with theone arc first, the vertex with the two arcs second, and the third vertex last.12. /G / /13. /H / /14. HG 15. The congruent sides that are included between congruent angles areand.16. Write a congruence statement. Justify your reasoning.n n99Lesson 4-3
Problem 2Writing a Proof Using ASACDGot It? Given: lCAB O lDAE, BA O EA, lB and lE are right anglesProve: kABC O kAEDA17. Complete the flow chart to prove nABC nAED.Given/B and /are right angles.BGivenGivenBA /CAB /All right angles are congruent.EASA PostulatenABC /B Theorem 4–2 Angle-Angle-Side (AAS) TheoremTheoremIf . . .Then . . .If two angles and anonincluded side of onetriangle are congruent to twoangles and the correspondingnonincluded side of anothertriangle, then the two trianglesare congruent./A /D, /B /E, AC DFnABC nDEFBFCD18. The nonincluded congruent sides of nABC and nDEF areEand.PProblem 3 Writing a Proof Using AASGot It? Given: lS O lQ, RP bisects lSRQSProve: kSRP O kQRP19. How do you know which angles in the diagram are corresponding angles?20. Complete the statements to provenSRP nQRP.StatementsReasons1) /S 1) Given2) RP bisects2) Given3) /SRP 3) Definition of an angle bisector4) RP 4) Reflexive Property of Congruence5) nSRP 5) AASChapter 4100QRCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.A
Problem 4Determining Whether Triangles Are Congruent21. The congruence marks show that /A IPGot It? Are kPAR and kSIR congruent? Explain.and PR .22. What other corresponding congruent parts exist? Explain.ARS23. Are nPAR and nSIR congruent? If so, what theorem proves them congruent?Lesson Check Do you UNDERSTAND?Reasoning Suppose lE O lI and FE O GI . What else must you know in order toprove kFDE and kGHI are congruent by ASA? By AAS?24. Label the diagram at the right.25. To prove the triangles congruent by ASA,what do you need?FCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.26. To prove the triangles congruent by AAS, what do you need?27. If you want to use ASA, /and /must also be congruent.28. If you want to use AAS, /and /must also be congruent.Math SuccessCheck off the vocabulary words that you understand.includednonincludedcorrespondingRate how well you can use ASA and AAS.Need toreview02468Now Iget it!10101Lesson 4-3
4-4Using Corresponding Partsof Congruent TrianglesVocabularyReviewUnderline the correct word(s) to complete each sentence.1. The Reflexive Property of Congruence states that any geometric figure iscongruent / similar to itself.2. The Reflexive Property of Equality states that any quantity isequal to / greater than / less than itself.3. Circle the expressions that illustrate the Reflexive Property of Equality.a5aIf AB 5 2, then 2 5 AB.3(x 1 y) 5 3x 1 3y51c551c4. Circle the expressions that illustrate the Reflexive Property of Congruence.If CD LM and LM XY, then CD XY./ABC /ABCCD CDVocabulary Builderproof (noun) proofRelated Word: prove (verb)Definition: A proof is convincing evidence that a statement or theory is true.Math Usage: A proof is a convincing argument that uses deductive reasoning.Use Your VocabularyComplete each statement with proof or prove.5. In geometry, a 9 uses definitions, postulates, and theorems toprove theorems.6. No one can 9 how our universe started.7. He can 9 when he bought the computer because he has a receipt.Chapter 4102Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.If /A /B, then /B /A.
D8. Complete the steps in the proof.Given: AB AD, BC DC,/D /B, /DAC /BACACProve: nABC nADCStatements1) AB BC 1) Given2) AC 3) /D BReasons2) Reflexive Property of /DAC 3) Given4) /DCA 4) Third Angles Theorem5) nABC 5) Definition of trianglesProblem 1 Proving Parts of Triangles CongruentCGot It? Given: BA O DA, CA O EAProve: lC O lECopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.9. Name four ways you can use congruent parts of twotriangles to prove that the triangles are congruent.EABD10. To prove triangles are congruent when you know two pairs of congruentcorresponding sides, you can useor.Underline the correct word to complete the sentence.11. The Given states and the diagram shows that there are one / two / threepairs of congruent sides.12. Give a reason for each statement of the proof.StatementsReasons1) BA DA1)2) CA EA2)3) /CAB /EAD3)4) nCAB nEAD4)5) /C /E5)103Lesson 4-4
Proving Triangle Parts Congruent to Measure DistanceProblem 2Got It? Given: AB O AC, M is the midpoint of BCBProve: lAMB O lAMCM13. Use the flow chart to complete the proof.CAReflexive Property of GivenGivenAB M is the midpoint ofAM .Definition of midpointBM SSS TheoremnAMB Corresponding parts of triangles are .Lesson Check Do you know HOW?Name the postulate or theorem that you can use to show the trianglesare congruent. Then explain why EA O MA.T14. Circle the angles that are marked congruent./E/ETA/M/EAT/MTAEA15. Circle the sides that are marked congruent.ETMTEAMAAT16. Circle the sides that are congruent by the Reflexive Property of Congruence.ET and MTEA and MAAT and AT17. Underline the correct postulate or theorem to complete the sentence.nEAT nMAT by SAS / AAS / ASA / SSS .18. Now explain why EA MA.Chapter 4104MCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved./AMB
Lesson Check Do you UNDERSTAND?KError Analysis Find and correct the error(s) in the proof.Given: KH NH, /L /MMHProve: H is the midpoint of LM .LProof: KH NH because it is given. /L /M because it is given./KHL /NHM because vertical angles are congruent. So, nKHL nMHNby ASA Postulate. Since corresponding parts of congruent triangles are congruent,LH MH . By the definition of midpoint, H is the midpoint of LM .NPlace a in the box if the statement is correct. Place an if it is incorrect.19. /KHL /NHM because vertical angels are congruent.20. nKHL nMHN by ASA Postulate.Underline the correct word to complete each sentence.21. When you name congruent triangles, you must name corresponding vertices ina different / the same order.22. To use the ASA Postulate, you need two pairs of congruent angles and a pair ofincluded / nonincluded congruent sides.23. To use the AAS Theorem, you need two pairs of congruent angles and a pair ofincluded / nonincluded congruent sides.24. Identify the error(s) in the proof.Copyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.25. Correct the error(s) in the proof.Math SuccessCheck off the vocabulary words that you understand.congruentcorrespondingproofRate how well you can use congruent triangles.Need toreview02468Now Iget it!10105Lesson 4-4
Isosceles andEquilateral Triangles4-5VocabularyReviewUnderline the correct word to complete each sentence.1. An equilateral triangle has two/ three congruent sides.2. An equilateral triangle has acute / obtuse angles.3. Circle the equilateral triangle.555385545Vocabulary Builderisoscelesisosceles (adjective) eye SAHS uh leezDefinition A triangle is isosceles if it has two congruent sides.Main Idea: The angles and sides of isosceles triangles havespecial relationships.Use Your Vocabulary4. Use the triangles below. Write the letter of each triangle in the correct circle(s)at the right.AEquilateralBDCEChapter 4106IsoscelesRightCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.Related Words: equilateral, scalene
Theorems 4–3, 4–4, 4–5Theorem 4-3 Isosceles Triangle TheoremIf two sides of a triangle are congruent, then the angles opposite thosesides are congruent.VertexAngleVertexAngleTheorem 4-4 Converse of Isosceles Triangle TheoremLegsLegsIf two angles of a triangle are congruent, then the sides opposite thoseangles are congruent.BaseBaseBaseAnglesBaseAnglesTheorem 4-5If a line bisects the vertex angle of an isosceles triangle, then the line is also theperpendicular bisector of the base.5. If PQ RQ in nPQR, then / /.6. Underline the correct theorem number to complete the sentence.The theorem illustrated below is Theorem 4–3 / 4–4 / 4–5 .CIf . . .ADCThen . . .BADBProblem 1 Using the Isosceles Triangle TheoremsTCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.Got It? Is lWVS congruent to lS? Is TR congruent to TS? Explain.7. The markings show that WV UW.R8. Is /WVS /S? Explain.VS9. Is/R /S? Explain.10. Is TR TS? Explain.107Lesson 4-5
Problem 2 Using AlgebraGot It? Suppose mlA 5 27. What is the value of x?11. Since CB A, nABC is isosceles.12. Since nABC is isosceles, m/A 5 m/5D.13. Since BD bisects the vertex of an isosceles triangle, BD 'and m/BDC 5Bx C.14. Use the justifications below to find the value of x.m/1 m/BDC 1x 5 1801Triangle Angle-Sum Theorem1x 5 180Substitute.1x 5 180Simplify.x5Subtract 117 from each side.Corollaries to Theorems 4–3 and 4–4Corollary to Theorem 4-3If a triangle is equilateral, then the triangle is equiangular.Corollary to Theorem 4-4If a triangle is equiangular, then the triangle is equilateral.15. Underline the correct number to complete the sentence.YIf . . .XYThen . . .ZXZProblem 3 Finding Angle MeasuresGot It? Suppose the triangles at the right are isosceles triangles,where lADE, lDEC, and lECB are vertex angles. If the vertexangles each have a measure of 58, what are mlA and mlBCD?16. Which triangles are congruent by the Side-Angle-Side Theorem?17. Which angles are congruent by the Isosceles Triangle Theorem?Chapter 4108DACEBCopyright by Pearson Education, Inc. or its affiliates. All Rights Reserved.The corollary illustrated below is Corollary to Theorem 4-3 / 4-4 .
18. By the Triangle Angle-Sum Theorem, m/A 1 58 1 m/DEA 5.19. Solve for m/A. /ECD, m/ECD 520. Since.21. Using the Angle Addition Postulate, m/BCD 5 58 1 m/ECD 5.Lesson Check Do you UNDERSTAND?What is the relationship between sides and angles for each type of triangle?isoscelesequilateralComplete.22. An isosceles triangle hascongruent sides.23.
Vocabulary Builder postulate (noun) PAHS chuh lit Definition: A postulate is a statement that is accepted as true without being proven true. Main Idea: In geometry, you use what you know to be true to prove new things true. The statements that you accept as true without proof are called postulates or axioms. Use Your Vocabulary 2. Underline the correct word to complete the sentence. You can .
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CHAPTER 4 Vocabulary List 1—Prefixes 31 CHAPTER 5 Vocabulary List 2—Suffixes 45 CHAPTER 6 Vocabulary List 3—Learning Roots 59 CHAPTER 7 Vocabulary List 4—More Roots 73 CHAPTER 8 Vocabulary List 5—Foreign Language Terms Used in English 87 CHAPTER 9 Vocabulary List 6—Business Terms 101
3rd Grade Math Vocabulary Resources 3rd Grade Math Vocabulary Resources contains two resources to promote student independence, develop math vocabulary, and support reading and writing in mathematics. All vocabulary is aligned with the Common Core State Standards. My Math Vocabulary Book contains over 190 essential math words for 3rd Grade.
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Building Vocabulary Skills, Short Version with Vocabulary Plus 978-1-59194-541-3 Improving Vocabulary Skills, Short Version with Vocabulary Plus 978-1-59194-542-0 Advancing Vocabulary Skills, Short Version with Vocabulary Plus 978-1-59194-543-7 PRINT compel unique destiny illuminate plausible vital impact affirm Eliza Comodromos Paul langan .
Vocabulary Power Plus for College and Career Readiness. 16 Vocabulary from Latin and Greek Roots. 17 Growing Your Vocabulary: Learning from Latin and Greek Roots . 17 Vocabulary for the College Bound. 17 Standards-Based Vocabulary Study
Rationale for teaching vocabulary, how to choose words to teach (Tier 1, Tier 2, Tier 3), how to teach vocabulary. Building Academic Vocabulary (Teacher’s Manual) by Robert Marzano & Debra J. Pickering; ASCD, 2005 Creating a list of academic vocabulary words how to teach them. Includes academic vocabulary word lists for content areas.
Vocabulary and Spelling snapshot and lessons Lessons From all WordFlyers levels 3 Topic Lessons Compound words 7.0.7 Spelling 7.3.4 Spelling 8.0.1 Spelling 9.3.2 Spelling 10.0.10 Spelling 10.1.6 Spelling Descriptive language adjectives 7.1.11 Vocabulary 8.0.4 Vocabulary 9.0.2 Vocabulary 10.0.1 Vocabulary Descriptive language adverbs
