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
   • ASA
   • SAS
2. 2.

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

   • ASA
   • AAS
   • Given
   • SAS

3. 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.

4. 3.

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

   • Given
   • Symmetric property
   • Reflexive property
   • CPCTC
5. 4.

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

   • Given
   • CPCTC
   • Reflexive property
   • Transitive property
6. 5.

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

   • Vertical angles theorem
   • CPCTC
   • Definition of angle bisector
   • Definition of midpoint

7. Use this

   Sketch, not to scale: triangles FCH and FVH share side FH; C is above FH and V is below. Marked: FC and FV with one tick each. Given: FC ≅ FV, and FH bisects ∠CFV. Prove: triangle FCH ≅ triangle FVH. Ladder: 1. FC ≅ FV -- Given; 2. FH bisects ∠CFV -- Given; 3. ∠CFH ≅ ∠VFH -- ?; 4. FH ≅ FH -- Reflexive property; 5. triangle FCH ≅ triangle FVH -- SAS.

8. 6.

   Kira sets a tent pole FH that splits the angle at F evenly. Which reason fills the blank?

   • Definition of midpoint
   • CPCTC
   • Vertical angles theorem
   • Definition of angle bisector
9. 7.

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

   • HC ≅ HY
   • HY ≅ HY
   • CY ≅ HQ
   • △HCY ≅ △HQY
10. 8.

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

    • GW ≅ DS
    • DG ≅ DW
    • DW ≅ DW
    • △DGW ≅ △DSW
11. 9.

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

    • DC ≅ YC
    • ∠DWC ≅ ∠WDC
    • ∠DWC ≅ ∠YWC
    • △WDC ≅ △WYC
12. 10.

    Pia draws a roof beam GU that splits the angle at G evenly. Which statement fills the blank?

    • FU ≅ HU
    • ∠FGU ≅ ∠HGU
    • △GFU ≅ △GHU
    • ∠FGU ≅ ∠GFU