Triangle proofs: fill in the missing step or reason
Grade 10 Math Worksheet - Challenge Me
Circle the best answer.
Kira sews a seam SY on a sail SUW; the two bottom pieces have lengths written with x. Which reason fills the blank?
- Subtraction property of equality
- Definition of midpoint
- Addition property of equality
- Multiplication property of equality
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
- Addition property of equality
- Definition of median
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.
Noah shows that the median CQ of road sign CDF splits its top angle evenly. Which statement fills the blank?
- CQ bisects ∠DCF
- CD ≅ DQ
- DQ ≅ FQ
- CQ ≅ DF
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.
Pia shows that the median SU of roof SWY splits its top angle evenly. Which statement fills the blank?
- SW ≅ WU
- WU ≅ YU
- SU bisects ∠WSY
- SU ≅ WY
Ren shows that the median GD of tent front GHV splits its top angle evenly. Which statement fills the blank?
- △GHD ≅ △GVD
- GD bisects ∠HGV
- △GHD ≅ △DVG
- △GHV ≅ △GVD
Tala shows that the median FY of pyramid face FCU splits its top angle evenly. Which statement fills the blank?
- △FCU ≅ △FUY
- FY bisects ∠CFU
- △FCY ≅ △FUY
- △FCY ≅ △YUF
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.
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
- ∠SQH ≅ ∠WQH — Reflexive property
- QH bisects ∠SQW — Definition of angle bisector
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.
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
- VC bisects ∠DVG — Definition of angle bisector
- ∠DVC ≅ ∠GVC — Reflexive property
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
- ∠CUG ≅ ∠FUG — CPCTC
- △UCG ≅ △UFG — SSS
- △UCG ≅ △GFU — SSS
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 ≅ △YSW — SSS
- ∠DYW ≅ ∠SYW — CPCTC
- △YDW ≅ △WSY — SSS
- △YDW ≅ △YSW — SAS