Geometry proof practice worksheet with ten problems involving triangle congruence, each with a diagram and given conditions.

1) Statement: AB || CD, AB ≅ CD; Reason: Given
2) Statement: ∠BAC ≅ ∠DCA; Reason: Alternate Interior Angles Theorem (AB || CD)
3) Statement: AC ≅ CA; Reason: Reflexive Property
4) Statement: ΔABC ≅ ΔDCB; Reason: SAS Congruence Postulate

1) Statement: ∠J ≅ ∠M, K is midpoint of JM; Reason: Given
2) Statement: JK ≅ MK; Reason: Definition of Midpoint
3) Statement: ∠JKN ≅ ∠MKL; Reason: Vertical Angles Theorem
4) Statement: ΔJKN ≅ ΔMKL; Reason: ASA Congruence Postulate

1) Statement: ∠X ≅ ∠W, ZT ⊥ XW; Reason: Given
2) Statement: ∠ZTX ≅ ∠ZTW; Reason: Definition of Perpendicular Lines (both are right angles)
3) Statement: ZT ≅ ZT; Reason: Reflexive Property
4) Statement: ΔXTZ ≅ ΔWTZ; Reason: AAS Congruence Theorem

1) Statement: RM ⊥ LP, RL ≅ RP; Reason: Given
2) Statement: ∠RML ≅ ∠RMP; Reason: Definition of Perpendicular Lines (both are right angles)
3) Statement: RM ≅ RM; Reason: Reflexive Property
4) Statement: ΔRML ≅ ΔRMP; Reason: HL Congruence Theorem (for right triangles)

1) Statement: AC bisects ∠BCD, BC ≅ DC; Reason: Given
2) Statement: ∠BCA ≅ ∠DCA; Reason: Definition of Angle Bisector
3) Statement: AC ≅ AC; Reason: Reflexive Property
4) Statement: ΔABC ≅ ΔADC; Reason: SAS Congruence Postulate

1) Statement: AB ≅ DC, AD ≅ BC; Reason: Given
2) Statement: BD ≅ DB; Reason: Reflexive Property
3) Statement: ΔABD ≅ ΔCDB; Reason: SSS Congruence Postulate

1) Statement: ∠R ≅ ∠U, ST bisects ∠RSU; Reason: Given
2) Statement: ∠RST ≅ ∠UST; Reason: Definition of Angle Bisector
3) Statement: ST ≅ ST; Reason: Reflexive Property
4) Statement: ΔRST ≅ ΔUST; Reason: AAS Congruence Theorem

1) Statement: ∠BDA and ∠BDC are right angles, BA ≅ BC; Reason: Given
2) Statement: BD ≅ BD; Reason: Reflexive Property
3) Statement: ΔBDA ≅ ΔBDC; Reason: HL Congruence Theorem (for right triangles)

1) Statement: RN ⊥ MP, N is midpoint of MP; Reason: Given
2) Statement: MN ≅ PN; Reason: Definition of Midpoint
3) Statement: ∠RNM ≅ ∠RNP; Reason: Definition of Perpendicular Lines (both are right angles)
4) Statement: RN ≅ RN; Reason: Reflexive Property
5) Statement: ΔRNM ≅ ΔRNP; Reason: SAS Congruence Postulate

1) Statement: ∠C ≅ ∠D, AB ⊥ CD; Reason: Given
2) Statement: ∠ABC ≅ ∠ABD; Reason: Definition of Perpendicular Lines (both are right angles)
3) Statement: AB ≅ AB; Reason: Reflexive Property
4) Statement: ΔABC ≅ ΔABD; Reason: AAS Congruence Theorem