Triangle proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Jun cuts a pizza slice CDF along median CQ; the two crust pieces have lengths written with x. Which reason fills the blank?

   • Subtraction property of equality
   • Substitution property
   • Addition property of equality
   • Division property of equality
2. 2.

   Kira sews a seam SY on a sail SUW; the two bottom pieces have lengths written with x. Which reason fills the blank?

   • Multiplication property of equality
   • Subtraction property of equality
   • Definition of midpoint
   • Addition property of equality
3. 3.

   Luz hangs a string HQ inside a tent front HGV; the two floor pieces have lengths written with x. Which reason fills the blank?

   • Division property of equality
   • Subtraction property of equality
   • Given
   • Substitution property
4. 4.

   Milo cuts a triangle sandwich DCY along median DS; the two edge pieces have lengths written with x. Which reason fills the blank?

   • Given
   • Division property of equality
   • Definition of median
   • Addition property of equality

5. Read this first

   Use this

   Given: CD ≅ CF, and CQ is a median of triangle CDF. Prove: CQ bisects ∠DCF. Ladder: 1. CD ≅ CF -- Given; 2. CQ is a median of triangle CDF -- Given; 3. Q is the midpoint of DF -- Definition of median; 4. ? -- Definition of midpoint; 5. CQ ≅ CQ -- Reflexive property; 6. triangle CDQ ≅ triangle CFQ -- SSS; 7. ∠DCQ ≅ ∠FCQ -- CPCTC; 8. CQ bisects ∠DCF -- Definition of angle bisector.

6. 5.

   Noah shows that the median CQ of road sign CDF splits its top angle evenly. Which statement fills the blank?

   • CD ≅ DQ
   • DQ ≅ FQ
   • CQ bisects ∠DCF
   • CQ ≅ DF
7. 6.

   Ren shows that the median GD of tent front GHV splits its top angle evenly. Which statement fills the blank?

   • △GHV ≅ △GVD
   • △GHD ≅ △DVG
   • △GHD ≅ △GVD
   • GD bisects ∠HGV

8. Use this

   Given: QS ≅ QW, and QH is a median of triangle QSW. Prove: QH bisects ∠SQW. Ladder: 1. QS ≅ QW -- Given; 2. QH is a median of triangle QSW -- Given; 3. H is the midpoint of SW -- Definition of median; 4. SH ≅ WH -- Definition of midpoint; 5. QH ≅ QH -- Reflexive property; 6. triangle QSH ≅ triangle QWH -- SSS; 7. ? -- ?; 8. QH bisects ∠SQW -- Definition of angle bisector.

9. 7.

   Zee shows that the seam QH of an isosceles sail QSW splits its top angle evenly. Which statement and reason fill the blanks?

   • ∠SQH ≅ ∠WQH — SSS
   • ∠SQH ≅ ∠WQH — CPCTC
   • QH bisects ∠SQW — Definition of angle bisector
   • ∠SQH ≅ ∠WQH — Reflexive property

10. Use this

    Given: VD ≅ VG, and VC is a median of triangle VDG. Prove: VC bisects ∠DVG. Ladder: 1. VD ≅ VG -- Given; 2. VC is a median of triangle VDG -- Given; 3. C is the midpoint of DG -- Definition of median; 4. DC ≅ GC -- Definition of midpoint; 5. VC ≅ VC -- Reflexive property; 6. triangle VDC ≅ triangle VGC -- SSS; 7. ? -- ?; 8. VC bisects ∠DVG -- Definition of angle bisector.

11. 8.

    Ari shows that the median VC of an isosceles ramp side VDG splits its top angle evenly. Which statement and reason fill the blanks?

    • ∠DVC ≅ ∠GVC — Reflexive property
    • ∠DVC ≅ ∠GVC — SSS
    • VC bisects ∠DVG — Definition of angle bisector
    • ∠DVC ≅ ∠GVC — CPCTC
12. 9.

    Bo shows that the median UG of an isosceles pizza slice UCF splits its tip angle evenly. Which statement and reason fill the blanks?

    • △UCG ≅ △UFG — SAS
    • △UCG ≅ △GFU — SSS
    • △UCG ≅ △UFG — SSS
    • ∠CUG ≅ ∠FUG — CPCTC
13. 10.

    Esme shows that the median YW of an isosceles road sign YDS splits its top angle evenly. Which statement and reason fill the blanks?

    • △YDW ≅ △WSY — SSS
    • △YDW ≅ △YSW — SSS
    • ∠DYW ≅ ∠SYW — CPCTC
    • △YDW ≅ △YSW — SAS