Congruent Figures
NameClass4-1DateStandardized Test PrepCongruent FiguresMultiple ChoiceFor Exercises 1–6, choose the correct letter.1. The pair of polygons at the right is congruent. What is m/J ?A4513590ABG135 CHF145DJ/A /DAB DE/B /EBC FDAECnSXF nGXTFF3. Given the diagram at the right, which of the followingmust be true? BnXSF nXTGDB2. The triangles at the right are congruent. Which of thefollowing statements must be true? InFXS nXGTXSnFXS nGXTGT4. If nRST nXYZ, which of the following need not be true? I/R /X/T /ZRT XZSR YZ5. If nABC nDEF , m/A 5 50, and m/E 5 30, what is m/C? C30501001206. If ABCD QRST , m/A 5 x 2 10, and m/Q 5 2x 2 30, what is m/A? F10Short Response203040[2] lABD O lCDB and lADB O lCBD, both by the Alt. Int AnglesThm. So, by Third Angles Thm., lA O lC . Because DB O BD by theRefl. Prop. of Congruence, and we know AB O CD and AD O CB, thenall the corresponding parts are congruent and kABD O kCDB.[1] incomplete proof [0] no proof or incorrect proofA7. Given: AB 6 DC , AD 6 BC , AB CD, AD CBBProve: nABD nCDBDPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.7C
NameClass4-2DateStandardized Test PrepTriangle Congruence by SSS and SASMultiple ChoiceFor Exercises 1–4, choose the correct letter.1. Which pair of triangles can be proved congruent by SSS? C2. Which pair of triangles can be proved congruent by SAS? GQ3. What additional information do you need toprove nNOP nQSR? DPN SQ/P /SNO QR/O /SSP4. What additional information do you need toprove nGHI nDEF ? FHI EF/F /GHI EDGI DFNROGEIFHDShort ResponseL5. Write a two-column proof.Given: M is the midpoint of LS, PM QM .Prove: nLMP nSMQMP[2] Statements: 1) M is the midpoint of LS; 2) LM O SM;3) lLMP O lSMQ; 4) PM O QM; 5) kLMP O kSMQ; Reasons:1) Given; 2) Def. of a midpoint; 3) Vert. ' are O; 4) Given;5) SAS [1] incomplete proof [0] incorrect or no proofPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.17QS
NameClassDateStandardized Test Prep4-3Triangle Congruence by ASA and AASMultiple ChoiceFor Exercises 1–4, choose the correct letter.1. Which pair of triangles can be proven congruent by the ASA Postulate? CLQRMNTVSPKWXUZYLGJHA2. For the ASA Postulate to apply, which side of the triangle must be known? Fthe included sidethe shortest sidethe longest sidea non-included side3. Which pair of triangles can be proven congruent by the AAS Theorem? DOLMKHGEB FJKC DAQRTSP4. For the AAS Theorem to apply, which side of the triangle must be known? Ithe included sidethe shortest sidethe longest sidea non-included sideWShort Response5. Write a paragraph proof.Given: /3 /5, /2 /4Prove: nVWX nVYXV51324YX[2] l3 O l5 is given.l1 O l5 because vert.' are O. l3 O l1 by theTrans. Prop. of O. l2 O l4is given. VX O VX by theRefl. Prop. of O.kVWX O kVYX by ASA.[1] incomplete proof[0] incorrect or no proofPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.27
NameClass4-4DateStandardized Test PrepUsing Corresponding Parts of Congruent TrianglesMultiple ChoiceFor Exercises 1–6, choose the correct letter.G1. Based on the given information in the figure at theright, how can you justify that nJHG nHJI ? BASAAASSSSASAHJIA2. In the figure at the right the following is true:B/ABD /CDB and /DBC /BDA. How canyou justify that nABD nCDB? HSASASASSSCPCTCDC3. nBRM nKYZ. How can you justify that YZ RM ? ACPCTCSASASASSS/BJP /IMTJP MI4. Which statement cannot be justified givenonly that nPBJ nTIM ? IPB TI/B /I5. In the figure at the right, which theorem or postulatecan you use to prove nADM nZMD? CASASASSSSAASAZMD6. In the figure at the right, which theorem or postulatecan you use to prove nKGC nFHE? HASASASSSSAASCEDKHGFShort Response7. What would a brief plan for the following proofABlook like?Given: AB DC, /ABC /DCBCProve: AC DBD[2] CB O BC by the Reflexive Property. kCBD O kBCA by SAS. AC O DB by CPCTC;[1] one step missing or one reason incorrect [0] incorrect or no responsePrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.37
NameClassDateStandardized Test Prep4-5Isosceles and Equilateral TrianglesGridded ResponseSolve each exercise and enter your answer on the grid provided.Refer to the diagram for Exercises 1–3.1. What is the value of x?y 125 x z 2. What is the value of y?3. What is the value of z?4. The measures of two of the sides of an equilateral triangle are 3x 1 15 in. and7x 2 5 in. What is the measure of the third side in inches?5. In nGHI , HI 5 GH , m/IHG 5 3x 1 4, and m/IGH 5 2x 2 24. What ism/HIG?Answers1.a 012345678901234567892.012345678901234567890 01 12 23 34 45 56 67 78 89 9a 012345678901234567893.012345678901234567890 01 12 23 34 45 56 67 78 89 9a 012345678901234567894.012345678901234567890 01 12 23 34 45 56 67 78 89 9a 012345678901234567895.012345678901234567890 01 12 23 34 45 56 67 78 89 9Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.47a 01234567890123456789012345678901234567890 01 12 23 34 45 56 67 78 89 9
NameClass4-6DateStandardized Test PrepCongruence in Right TrianglesMultiple ChoiceFor Exercises 1–4, choose the correct letter.1. Which additional piece of information would allow you toDAprove that the triangles are congruent by the HL theorem? Cm/DFE 5 40AB DEm/F 5 m/ABCAC DFFCBE2. For what values of x and y are the triangles shown congruent? F10xx 5 1, y 5 38x 5 2, y 5 4 x 5 4, y 5 12xx 5 1, y 5 410x yy 2x3. Two triangles have two pairs of corresponding sides that arecongruent. What else must be true for the triangles to becongruent by the HL Theorem? DThe included angles must be right angles.They have one pair of congruent angles.Both triangles must be isosceles.There are right angles adjacent to just one pair of congruent sides.4. Which of the following statements is true? HAnBAC nGHI by SAS.nDEF nGHI by SAS.nBAC nDEF by HL.BCFDGHEInDEF nGHI by HL.Extended Response5. Are the given triangles congruent by the HL Theorem? Explain.[4] No; they are right triangles, and have a pair of congruentlegs (AB O BC), but the hypotenuses, DB and DC , are notcongruent. So, the triangles only meet two of the threeconditions for congruence by the HL Theorem.[3] appropriate response plus a discussion of two of thethree criteria for congruence [2] recognition only thatthe hypotenuses are not congruent [1] recognition that thetriangles are not congruent [0] incorrect or no responseDBCPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.57A
NameClass4-7DateStandardized Test PrepCongruence in Overlapping TrianglesMultiple ChoiceFor Exercises 1–5, choose the correct letter.1. What is the common angle of nPQT and nRSQ? A/PQT/SRQ/SPT/SUTPSQUTRZUse the following information for Exercises 2–5.YRGiven: nZWX nYXW , ZW 6 YXProve: nZWR nYRXWX2. Which corresponding parts statement is needed toprove nZWR nYRX ? H/ZWR /YXRZW 5 YX/Z /RWX 5 WX3. A classmate writes the statement /ZRW /YRX to help prove thecongruence of the triangles. What reason should the classmate give? DGivenAngles cut by a bisector are congruent.Base angles of an isosceles triangle are congruent.Vertical angles are congruent.4. After using the congruence statements from Exercises 2 and 3, whichstatement can be used to prove the triangles congruent? F/Z /YWX WX/ZWR /RYXWR RX5. Which theorem or postulate will prove nZWR nYRX ? DSASSSSASAAASShort ResponseE6. In the diagram at the right, which two triangles should beproved congruent first to help prove nABF nEDF ?DC[2] kACD and kECB [1] Correct named but vertices donot correspond. [0] incorrect namedPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.67FBA
For what values of x and y are the triangles shown congruent? x 5 1, y 5 4 x 5 4, y 5 1 x 5 2, y 5 4 x 5 1, y 5 3 3. Two triangles have two pairs of corresponding sides that are congruent. What else must be true for the triangles to be congruent by the HL ! eorem?! e included angles must be right angles.
F It has 3 congruent rectangles. G It has 3 rectangles that are not congruent. H It has 4 congruent rectangles. J It has 4 rectangles and none are congruent. 7. JKL is congruent to RST . L and T are r
Feb 14, 2011 · Ch 4: Congruent Triangles 4‐1 Congruent Figures 4‐2 Triangle Congruence by SSS and SAS 4‐3 Triangle Congruence by ASA and AAS 4‐4 Using Congruent Triangles: CPCTC 4‐5 Isosceles and Equilateral Triangles 4‐6 Congruence in Right Triangles 4‐7 Using Corresponding Parts of Congruent Triangles
Once we prove triangles are congruent, we know that their corresponding parts (angles and sides) are congruent. We can abbreviate this is in a proof by using the reasoning of: CPCTC (Corresponding Parts of Congruent Triangles are Congruent). To Prove Angles or Sides Congruent: 1. Prove the triangles are congruent (using one of the above .
Unit 2 Congruence Congruent Triangles Textbook section IXL skills Lesson 1: Congruent Parts, Part 1 1.Corresponding parts of congruent polygons UDW Lesson 2: Congruent Parts, Part 2 1.Solve problems involving corresponding parts WYB Lesson 3: Congruent Triangles, Part 1 Lesson 4: Congruent Tr
Congruent Triangles Identify corresponding parts of congruent figures and be able to prove triangles congruent using SSS, ASA, SAS, AAS, and HL. Use congruent triangles to prove that the corresponding parts are congruent. Apply theorems about isosceles triangles and use the definition and theorems in proofs.
The two figures are not congruent. b. Determine if the two figures are congruent by using transformations. Explain your reasoning. If you have two congruent figures, you can determine the transformation, or series of transformations, that maps one figure onto the other by analyzing the orientation or relative position of the figures.
Congruent Triangles Strand: Triangles Topic: Exploring congruent triangles, using constructions, proofs, and coordinate methods Primary SOL: G.6 The student, given information in the form of a figure or statement will prove two triangles are congruent. Related SOL: G.4, G.5 Materials Congruent Triangles: Shortcuts activity sheet (attached)
Sep 03, 2013 · AAS Theorem Another way to show that two triangles are congruent is the Angle-Angle-Side (AAS) Theorem. AAS Theorem If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. You now have five ways to show that two triangles are congruent.
