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?

   • Addition property of equality
   • Division property of equality
   • Subtraction property of equality
   • Substitution property
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?

   • Definition of midpoint
   • Addition property of equality
   • Subtraction property of equality
   • Multiplication 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?

   • Substitution property
   • Subtraction property of equality
   • Division property of equality
   • Given
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?

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

5. Read this first

   Use this

   Sketch, not to scale: triangle SWY with S at the top and base WY; segment SU runs from S to point U on WY. Marked: SW and SY with one tick each. Given: SW ≅ SY, and SU is a median of triangle SWY. Prove: SU bisects ∠WSY. Ladder: 1. SW ≅ SY -- Given; 2. SU is a median of triangle SWY -- Given; 3. U is the midpoint of WY -- Definition of median; 4. ? -- Definition of midpoint; 5. SU ≅ SU -- Reflexive property; 6. triangle SWU ≅ triangle SYU -- SSS; 7. ∠WSU ≅ ∠YSU -- CPCTC; 8. SU bisects ∠WSY -- Definition of angle bisector.

6. 5.

   Pia shows that the median SU of roof SWY splits its top angle evenly. Which statement fills the blank?

   • SU bisects ∠WSY
   • SW ≅ WU
   • WU ≅ YU
   • SU ≅ WY
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 ≅ △GVD
   • GD bisects ∠HGV
   • △GHD ≅ △DVG
8. 7.

   Tala shows that the median FY of pyramid face FCU splits its top angle evenly. Which statement fills the blank?

   • FY bisects ∠CFU
   • △FCY ≅ △FUY
   • △FCY ≅ △YUF
   • △FCU ≅ △FUY

9. 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.

10. 8.

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

11. 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.

12. 9.

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

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