Congruence proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Ren checks whether two pizza slices CDF and GHQ match. Which reason fills the blank?

   • Given
   • SSS
   • SAS
   • ASA
2. 2.

   Tala checks whether two tent flaps CDF and GHQ match. Which reason fills the blank?

   • ASA
   • SAS
   • AAS
   • Given
3. 3.

   Zee checks whether two triangle signs CDF and GHQ match. Which reason fills the blank?

   • Given
   • SSS
   • ASA
   • AAS
4. 4.

   Ari checks whether two sandwich halves CDF and GHQ match. Which reason fills the blank?

   • Given
   • SSS
   • HL
   • SAS

5. Read this first

   Use this

   Given: CD ≅ CG and DF ≅ GF. Prove: triangle CDF ≅ triangle CGF. Ladder: 1. CD ≅ CG -- Given; 2. DF ≅ GF -- Given; 3. CF ≅ CF -- ?; 4. triangle CDF ≅ triangle CGF -- SSS.

6. 5.

   Bo builds a kite from two triangles, CDF and CGF, that share stick CF. Which reason fills the blank?

   • Reflexive property
   • Symmetric property
   • CPCTC
   • Given
7. 6.

   Esme sews two triangle sails, SVU and SWU, that share edge SU. Which reason fills the blank?

   • Reflexive property
   • Given
   • Transitive property
   • CPCTC
8. 7.

   Jun builds a kite whose stick QS splits the top angle evenly. Which reason fills the blank?

   • Vertical angles theorem
   • Definition of midpoint
   • CPCTC
   • Definition of angle bisector
9. 8.

   Luz sews two triangle patches, HCY and HQY, that share seam HY. Which statement fills the blank?

   • HC ≅ HY
   • △HCY ≅ △HQY
   • HY ≅ HY
   • CY ≅ HQ
10. 9.

    Milo folds paper so triangles DGW and DSW share fold DW. Which statement fills the blank?

    • DW ≅ DW
    • △DGW ≅ △DSW
    • DG ≅ DW
    • GW ≅ DS
11. 10.

    Noah builds a kite whose stick WC splits the angle at W evenly. Which statement fills the blank?

    • △WDC ≅ △WYC
    • DC ≅ YC
    • ∠DWC ≅ ∠WDC
    • ∠DWC ≅ ∠YWC