Congruent Triangles: Missing Reasons Activity
CongruentTriangles: MissingReasons Activity
Name: Answer Key Hour: Date:Directions: Choose the missing reasons from the box below each proof and writethem next to their corresponding statement. Not all the reasons will be used.DGiven: B is the midpoint of AC, AD CDProve: DAB ACDBBStatementsCReasons1. B is the midpoint of AC, AD CDGiven2. AB CBDefinition of midpoint3. DB DBReflexive Property4.ADB CDBSSSDefinition of right triangleDefinition of midpointReflexive PropertyGiven: AD CB ; ADProve: ADB lines form right anglesHLPSBCBDPSSSSADStatements1. AD CB ; ADGivenCReasonsGiven2. ADB CBDAlternate interior angle are congruent3. DB DBReflexive Property4. ADB CBDSASAlternate interior angle are congruentDefinition of midpointSASReflexive PropertyVertical angles are congruentASAGiven ("Secondary Math Shop") 2013
XGiven: T is the midpoint of SW ;SR WXSTProve: SRT WXTWRStatementsReasons1. T is the midpoint of SW ;SRWXGiven2. ST WTDefinition of midpoint3. SRT WXTAlternate interior angles are congruent4. RTS XTWVertical angles are congruent5. SRT AASWXTAASAlternate interior angle are congruentReflexive PropertyDefinition of midpointConsecutive interior angles are congruentGivenSASVertical angles are congruentASAOCGiven: OACE ; AB CBProve: AOB BACEBEStatements1. OAReasonsGivenCE ; AB CB2. OAB CEBAlternate interior angles are congruent3. ABO CBEVertical angles are congruent4. AOB ASACEBConsecutive interior angles are congruentAlternate interior angles are congruentASADefinition of midpointVertical angles are congruentAASGiven ("Secondary Math Shop") 2013
SGiven: PR SQ ; PQ PSProve: PRQ RPPRSQStatementsReasonsGiven1. PR SQ2. PRQ and PRS are right angles lines form right angles3.Definition of right trianglePRQ andPRS are right triangles4. PQ PSGiven5. PR PRReflexive Property6. PRQ PRSHL lines form right anglesGivenDefinition of right triangleReflexive PropertySSSDefinition of midpointAlternate interior angles are congruentHLASAGivenVertical angles are congruentAGiven: BC AD ; BD ACBProve: BAC ABDDStatementsCReasons1. BC AD ; BD ACGiven2. AB BAReflexive Property3.BAD ABCSSS4. BAC ABDASASSSCPCTCAASGivenCPCTCDefinition of midpointDefinition of segment bisectorAlternate interior angles are congruentReflexive Property ("Secondary Math Shop") 2013
XWGiven: WY and XZ bisecteach other at PPProve: WPX YPZZYStatements1: WY and XZ bisecteach other at PGiven2. WP YP ; XP ZPDefinition of segment bisector3. ADB CBDVertical angles are congruent4. WPX SASGivenSSSReasonsSASYPZASADefinition of segment bisectorDefinition of angle bisectorVertical angles are congruentYGiven: XZ bisects YXWand YZWProve: XYZ Definition of midpointXXWZZWStatements1. XZ bisects YXWand YZWGiven2. YXZ WXZDefinition of angle bisector3. YZX WZXDefinition of angle bisector4. XZ XZReflexive Property5. XYZ XWZDefinition of midpointSSSReasonsASADefinition of segment bisectorVertical angles are congruentASASASReflexive PropertyDefinition of angle bisectorGiven ("Secondary Math Shop") 2013
DGiven: 1 2 ; 3 43Prove: AB CDC21 4BAStatementsReasons1. 1 2 ; 3 4Given2. DB DBReflexive Property3. ABD ASACDBCPCTC4. AB CDDefinition of midpointReflexive PropertySSSCPCTCDefinition of segment bisectorASADefinition of angle bisectorSASGivenAGiven: AC BD ; AB ADProve: BAC DACBCStatementsReasons1. AC BD ; AB ADGiven2. ACB and ACD are right angles lines form right angles3. ACB ACDAll right angles are congruent4. AC ACReflexive5. ABC 6.ADCHL BAC DAC lines form right anglesCPCTCGivenDefinition of right triangleVertical angles are congruentReflexive PropertyDefinition of midpointASAHLSSSCPCTCAll right angles are congruent ("Secondary Math Shop") 2013
Name: Hour: Date:Directions: Choose the missing reasons from the box below each proof and writethem next to their corresponding statement. Not all the reasons will be used.DGiven: B is the midpoint of AC, AD CDProve: DAB ACDBBStatementsCReasons1. B is the midpoint of AC, AD CD2. AB CB3. DB DB4.ADB CDBDefinition of right triangleDefinition of midpoint lines form right anglesReflexive PropertyGiven: AD CB ; ADProve: ADB HLPSGivenBACBDDStatements1. AD CB ; ADSSSCReasonsPS2. ADB CBD3. DB DB4. ADB CBDAlternate interior angle are congruentDefinition of midpointSASReflexive PropertyVertical angles are congruentASAGiven ("Secondary Math Shop") 2013
XGiven: T is the midpoint of SW ;SR WXSTProve: SRT WXTWRStatementsReasons1. T is the midpoint of SW ;SRWX2. ST WT3. SRT WXT4. RTS XTW5. SRT WXTAASAlternate interior angle are congruentReflexive PropertyDefinition of midpointConsecutive interior angles are congruentGivenSASVertical angles are congruentASAOCGiven: OACE ; AB CBBProve: AOB ACEBEStatements1. OAReasonsCE ; AB CB2. OAB CEB3. ABO CBE4. AOB CEBConsecutive interior angles are congruentAlternate interior angles are congruentASADefinition of midpointVertical angles are congruentAASGiven ("Secondary Math Shop") 2013
SGiven: PR SQ ; PQ PSProve: PRQ RPPRSQStatementsReasons1. PR SQ2. PRQ and PRS are right angles3.PRQ andPRS are right triangles4. PQ PS5. PR PR6. PRQ PRS lines form right anglesGivenDefinition of right triangleReflexive PropertyDefinition of midpointAlternate interior angles are congruentHLSSSASAGivenVertical angles are congruentAGiven: BC AD ; BD ACBProve: BAC ABDDStatementsCReasons1. BC AD ; BD AC2. AB BA3.BAD ABC4. BAC ABDASASSSCPCTCAASGivenDefinition of midpointDefinition of segment bisectorAlternate interior angles are congruentReflexive Property ("Secondary Math Shop") 2013
XWGiven: WY and XZ bisecteach other at PPProve: WPX YPZZYStatementsReasons1: WY and XZ bisecteach other at P2. WP YP ; XP ZP3. ADB CBD4. WPX GivenSSSSASYPZASADefinition of segment bisectorDefinition of angle bisectorVertical angles are congruentYGiven: XZ bisects YXWand YZWProve: XYZ Definition of midpointXXWZZWStatementsReasons1. XZ bisects YXWand YZW2. YXZ WXZ3. YZX WZX4. XZ XZ5. XYZ XWZDefinition of midpointSSSDefinition of segment bisectorVertical angles are congruentASASASReflexive PropertyDefinition of angle bisectorGiven ("Secondary Math Shop") 2013
DGiven: 1 2 ; 3 43Prove: AB CDC21 4BAStatementsReasons1. 1 2 ; 3 42. DB DB3. ABD CDB4. AB CDDefinition of midpointReflexive PropertySSSCPCTCDefinition of segment bisectorASADefinition of angle bisectorSASGivenAGiven: AC BD ; AB ADProve: BAC DACBCStatementsReasons1. AC BD ; AB AD2. ACB and ACD are right angles3. ACB ACD4. AC AC5. ABC 6.ADC BAC DAC lines form right anglesGivenDefinition of right triangleVertical angles are congruentReflexive PropertyDefinition of midpointASAHLSSSCPCTCAll right angles are congruent ("Secondary Math Shop") 2013
Name: Hour: Date:Directions: Complete each proof below by supplying the missing reasons. Be sureto mark the given information on the diagrams to assist you.DGiven: B is the midpoint of AC, AD CDProve: DAB ACDBBStatementsCReasons1. B is the midpoint of AC, AD CD2. AB CB3. DB DB4.ADB CDBGiven: AD CB ; ADProve: ADB CBDStatements1. AD CB ; ADPSBADCReasonsPS2. ADB CBD3. DB DB4. ADB CBD ("Secondary Math Shop") 2013
XGiven: T is the midpoint of SW ;SR WXSTProve: SRT WXTWRStatementsReasons1. T is the midpoint of SW ;SRWX2. ST WT3. SRT WXT4. RTS XTW5. SRT WXTOCGiven: OACE ; AB CBBProve: AOB Statements1. OACEBAEReasonsCE ; AB CB2. OAB CEB3. ABO CBE4. AOB CEB ("Secondary Math Shop") 2013
SGiven: PR SQ ; PQ PSProve: PRQ PRSRPQStatementsReasons1. PR SQ2. PRQ and PRS are right angles3.PRQ andPRS are right triangles4. PQ PS5. PR PR6. PRQ PRSAGiven: BC AD ; BD ACBProve: BAC ABDDStatementsCReasons1. BC AD ; BD AC2. AB BA3.BAD ABC4. BAC ABD ("Secondary Math Shop") 2013
XWGiven: WY and XZ bisecteach other at PPProve: WPX YPZZYStatementsReasons1: WY and XZ bisecteach other at P2. WP YP ; XP ZP3. ADB CBD4. WPX YPZYGiven: XZ bisects YXWand YZWProve: XYZ XWZXZWStatementsReasons1. XZ bisects YXWand YZW2. YXZ WXZ3. YZX WZX4. XZ XZ5. XYZ XWZ ("Secondary Math Shop") 2013
DGiven: 1 2 ; 3 4Prove: AB CD3C21 4BAStatementsReasons1. 1 2 ; 3 42. DB DB3. ABD CDB4. AB CDAGiven: AC BD ; AB ADProve: BAC DACStatementsBCReasons1. AC BD ; AB AD2. ACB and ACD are right angles3. ACB ACD4. AC AC5. ABC 6.ADC BAC DAC ("Secondary Math Shop") 2013
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("Secondary Math Shop") 2013 Given 2. 3. Vertical angles are congruent 1. 2. 3. Given: T i
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
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)
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 .
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.
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.
Jul 05, 2018 · Congruent Triangles Reasoning and Proof Reasoning and proof of congruent triangles involves proving congruence of at least two triangles according to five congruent triangles theorems (Secondary School Mathematics Section by People’s Education Press, 2013). The five congruent triangles theorems have the following types: 1.
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
3. Is it possible to construct two triangles that are not congruent? 4. Which of the following applies to your triangle: SSS, SAS, ASA, AAS, SSA, or AAA? 5. Write a conjecture (prediction) about two triangles with right angles, congruent hypotenuses, and one pair of congruent legs.
