Congruent Triangles Worksheet for 10th Grade | Lesson Planet - Free Printable

1. Given: UW ≅ WX, VW ≅ VX
Prove: ∠UVW ≅ ∠UXV
Proof:
- UW ≅ WX (Given)
- VW ≅ VX (Given)
- UV ≅ UX (Reflexive Property)
- △UVW ≅ △UXV (SSS Congruence)
- ∠UVW ≅ ∠UXV (CPCTC)

2. Given: QW ≅ RW, SW ≅ TW
Prove: △QSW ≅ △RTW
Proof:
- QW ≅ RW (Given)
- SW ≅ TW (Given)
- ∠QWS ≅ ∠RWT (Vertical Angles)
- △QSW ≅ △RTW (SAS Congruence)

3. Given: AB ≅ CD, AD ≅ CB
Prove: ∠A ≅ ∠C
Proof:
- AB ≅ CD (Given)
- AD ≅ CB (Given)
- BD ≅ DB (Reflexive Property)
- △ABD ≅ △CDB (SSS Congruence)
- ∠A ≅ ∠C (CPCTC)

4. Given: LM ≅ MN, LP ≅ NP
Prove: ∠LPM ≅ ∠NPM
Proof:
- LM ≅ MN (Given)
- LP ≅ NP (Given)
- MP ≅ PM (Reflexive Property)
- △LPM ≅ △NPM (SSS Congruence)
- ∠LPM ≅ ∠NPM (CPCTC)

5. Given: QR ≅ ST, QS ≅ RT
Prove: ∠Q ≅ ∠T
Proof:
- QR ≅ ST (Given)
- QS ≅ RT (Given)
- RS ≅ SR (Reflexive Property)
- △QRS ≅ △TSR (SSS Congruence)
- ∠Q ≅ ∠T (CPCTC)

6. Given: AB ≅ DE, AC ≅ DF, BC ≅ EF
Prove: △ABC ≅ △DEF
Proof:
- AB ≅ DE (Given)
- AC ≅ DF (Given)
- BC ≅ EF (Given)
- △ABC ≅ △DEF (SSS Congruence)

7. Given: ∠A ≅ ∠D, AB ≅ DE, AC ≅ DF
Prove: △ABC ≅ △DEF
Proof:
- ∠A ≅ ∠D (Given)
- AB ≅ DE (Given)
- AC ≅ DF (Given)
- △ABC ≅ △DEF (SAS Congruence)

8. Given: ∠B ≅ ∠E, BC ≅ EF, AB ≅ DE
Prove: △ABC ≅ △DEF
Proof:
- ∠B ≅ ∠E (Given)
- BC ≅ EF (Given)
- AB ≅ DE (Given)
- △ABC ≅ △DEF (SAS Congruence)