Geometry Files: Triangle Congruence - Insert Clever Math Pun Here - Free Printable
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Step-by-step solution for: Geometry Files: Triangle Congruence - Insert Clever Math Pun Here
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Step-by-step solution for: Geometry Files: Triangle Congruence - Insert Clever Math Pun Here
1) Given: AB ∥ CD; AB ≅ CD
Prove: ΔABC ≅ ΔDCB
Statement Reason
1. AB ∥ CD Given
2. AB ≅ CD Given
3. ∠ABC ≅ ∠DCB Alternate Interior Angles Theorem (AB ∥ CD, transversal BC)
4. BC ≅ CB Reflexive Property of Congruence
5. ΔABC ≅ ΔDCB SAS Postulate (Steps 2, 3, 4)
2) Given: ∠J ≅ ∠M, K is midpoint of JM
Prove: ΔJKN ≅ ΔMKL
Statement Reason
1. ∠J ≅ ∠M Given
2. K is midpoint of JM Given
3. JK ≅ MK Definition of Midpoint
4. ∠JKN ≅ ∠MKL Vertical Angles Theorem
5. ΔJKN ≅ ΔMKL ASA Postulate (Steps 1, 3, 4)
3) Given: ∠X ≅ ∠W, ZT ⊥ XW
Prove: ΔXTZ ≅ ΔWTZ
Statement Reason
1. ∠X ≅ ∠W Given
2. ZT ⊥ XW Given
3. ∠ZTX ≅ ∠ZTW Definition of Perpendicular Lines (both are right angles)
4. ZT ≅ ZT Reflexive Property of Congruence
5. ΔXTZ ≅ ΔWTZ AAS Theorem (Steps 1, 3, 4)
4) Given: RM ⊥ LP; RL ≅ RP
Prove: ΔRML ≅ ΔRMP
Statement Reason
1. RM ⊥ LP Given
2. RL ≅ RP Given
3. ∠RML ≅ ∠RMP Definition of Perpendicular Lines (both are right angles)
4. RM ≅ RM Reflexive Property of Congruence
5. ΔRML ≅ ΔRMP HL Theorem (Steps 2, 3, 4)
5) Given: AC bisects ∠BCD; BC ≅ DC
Prove: ΔABC ≅ ΔADC
Statement Reason
1. AC bisects ∠BCD Given
2. BC ≅ DC Given
3. ∠BCA ≅ ∠DCA Definition of Angle Bisector
4. AC ≅ AC Reflexive Property of Congruence
5. ΔABC ≅ ΔADC SAS Postulate (Steps 2, 3, 4)
6) Given: AB ≅ DC; AD ≅ BC
Prove: ΔABD ≅ ΔCDB
Statement Reason
1. AB ≅ DC Given
2. AD ≅ BC Given
3. BD ≅ DB Reflexive Property of Congruence
4. ΔABD ≅ ΔCDB SSS Postulate (Steps 1, 2, 3)
7) Given: ∠R ≅ ∠U; ST bisects ∠RSU
Prove: ΔRST ≅ ΔUST
Statement Reason
1. ∠R ≅ ∠U Given
2. ST bisects ∠RSU Given
3. ∠RST ≅ ∠UST Definition of Angle Bisector
4. ST ≅ ST Reflexive Property of Congruence
5. ΔRST ≅ ΔUST AAS Theorem (Steps 1, 3, 4)
8) Given: ∠BDA and ∠BDC are right angles; BA ≅ BC
Prove: ΔBDA ≅ ΔBDC
Statement Reason
1. ∠BDA and ∠BDC are right angles Given
2. BA ≅ BC Given
3. ∠BDA ≅ ∠BDC All right angles are congruent
4. BD ≅ BD Reflexive Property of Congruence
5. ΔBDA ≅ ΔBDC HL Theorem (Steps 2, 3, 4)
9) Given: RN ⊥ MP; N is midpoint of MP
Prove: ΔRNM ≅ ΔRNP
Statement Reason
1. RN ⊥ MP Given
2. N is midpoint of MP Given
3. MN ≅ PN Definition of Midpoint
4. ∠RNM ≅ ∠RNP Definition of Perpendicular Lines (both are right angles)
5. RN ≅ RN Reflexive Property of Congruence
6. ΔRNM ≅ ΔRNP SAS Postulate (Steps 3, 4, 5)
10) Given: ∠C ≅ ∠D; AB ⊥ CD
Prove: ΔABC ≅ ΔABD
Statement Reason
1. ∠C ≅ ∠D Given
2. AB ⊥ CD Given
3. ∠ABC ≅ ∠ABD Definition of Perpendicular Lines (both are right angles)
4. AB ≅ AB Reflexive Property of Congruence
5. ΔABC ≅ ΔABD AAS Theorem (Steps 1, 3, 4)
Prove: ΔABC ≅ ΔDCB
Statement Reason
1. AB ∥ CD Given
2. AB ≅ CD Given
3. ∠ABC ≅ ∠DCB Alternate Interior Angles Theorem (AB ∥ CD, transversal BC)
4. BC ≅ CB Reflexive Property of Congruence
5. ΔABC ≅ ΔDCB SAS Postulate (Steps 2, 3, 4)
2) Given: ∠J ≅ ∠M, K is midpoint of JM
Prove: ΔJKN ≅ ΔMKL
Statement Reason
1. ∠J ≅ ∠M Given
2. K is midpoint of JM Given
3. JK ≅ MK Definition of Midpoint
4. ∠JKN ≅ ∠MKL Vertical Angles Theorem
5. ΔJKN ≅ ΔMKL ASA Postulate (Steps 1, 3, 4)
3) Given: ∠X ≅ ∠W, ZT ⊥ XW
Prove: ΔXTZ ≅ ΔWTZ
Statement Reason
1. ∠X ≅ ∠W Given
2. ZT ⊥ XW Given
3. ∠ZTX ≅ ∠ZTW Definition of Perpendicular Lines (both are right angles)
4. ZT ≅ ZT Reflexive Property of Congruence
5. ΔXTZ ≅ ΔWTZ AAS Theorem (Steps 1, 3, 4)
4) Given: RM ⊥ LP; RL ≅ RP
Prove: ΔRML ≅ ΔRMP
Statement Reason
1. RM ⊥ LP Given
2. RL ≅ RP Given
3. ∠RML ≅ ∠RMP Definition of Perpendicular Lines (both are right angles)
4. RM ≅ RM Reflexive Property of Congruence
5. ΔRML ≅ ΔRMP HL Theorem (Steps 2, 3, 4)
5) Given: AC bisects ∠BCD; BC ≅ DC
Prove: ΔABC ≅ ΔADC
Statement Reason
1. AC bisects ∠BCD Given
2. BC ≅ DC Given
3. ∠BCA ≅ ∠DCA Definition of Angle Bisector
4. AC ≅ AC Reflexive Property of Congruence
5. ΔABC ≅ ΔADC SAS Postulate (Steps 2, 3, 4)
6) Given: AB ≅ DC; AD ≅ BC
Prove: ΔABD ≅ ΔCDB
Statement Reason
1. AB ≅ DC Given
2. AD ≅ BC Given
3. BD ≅ DB Reflexive Property of Congruence
4. ΔABD ≅ ΔCDB SSS Postulate (Steps 1, 2, 3)
7) Given: ∠R ≅ ∠U; ST bisects ∠RSU
Prove: ΔRST ≅ ΔUST
Statement Reason
1. ∠R ≅ ∠U Given
2. ST bisects ∠RSU Given
3. ∠RST ≅ ∠UST Definition of Angle Bisector
4. ST ≅ ST Reflexive Property of Congruence
5. ΔRST ≅ ΔUST AAS Theorem (Steps 1, 3, 4)
8) Given: ∠BDA and ∠BDC are right angles; BA ≅ BC
Prove: ΔBDA ≅ ΔBDC
Statement Reason
1. ∠BDA and ∠BDC are right angles Given
2. BA ≅ BC Given
3. ∠BDA ≅ ∠BDC All right angles are congruent
4. BD ≅ BD Reflexive Property of Congruence
5. ΔBDA ≅ ΔBDC HL Theorem (Steps 2, 3, 4)
9) Given: RN ⊥ MP; N is midpoint of MP
Prove: ΔRNM ≅ ΔRNP
Statement Reason
1. RN ⊥ MP Given
2. N is midpoint of MP Given
3. MN ≅ PN Definition of Midpoint
4. ∠RNM ≅ ∠RNP Definition of Perpendicular Lines (both are right angles)
5. RN ≅ RN Reflexive Property of Congruence
6. ΔRNM ≅ ΔRNP SAS Postulate (Steps 3, 4, 5)
10) Given: ∠C ≅ ∠D; AB ⊥ CD
Prove: ΔABC ≅ ΔABD
Statement Reason
1. ∠C ≅ ∠D Given
2. AB ⊥ CD Given
3. ∠ABC ≅ ∠ABD Definition of Perpendicular Lines (both are right angles)
4. AB ≅ AB Reflexive Property of Congruence
5. ΔABC ≅ ΔABD AAS Theorem (Steps 1, 3, 4)
Parent Tip: Review the logic above to help your child master the concept of triangle proofs worksheet with answers.
