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10th grade Triangle proofs: fill in the missing step or reason worksheet

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Triangle proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Challenge Me

NameDate

Circle the best answer.

  1. 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
    • Addition property of equality
    • Definition of midpoint
    • Subtraction property of equality

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

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

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

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

  4. 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.

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

    • DQ ≅ FQ
    • CD ≅ DQ
    • CQ ≅ DF
    • CQ bisects ∠DCF

  6. 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.

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

    • SW ≅ WU
    • SU ≅ WY
    • SU bisects ∠WSY
    • WU ≅ YU

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

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

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

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

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

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

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

  13. 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 — SAS
    • △YDW ≅ △YSW — SSS
    • △YDW ≅ △WSY — SSS
    • ∠DYW ≅ ∠SYW — CPCTC
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10th grade Triangle proofs: fill in the missing step or reason worksheet – printable
Print: 123456

About this worksheet

Triangle proofs: fill in the missing step or reason. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can name the reason for each step of a proof about a triangle's angles, sides, midsegment or median.
  • I can tell the base angles theorem from its converse.
  • I can name the property of equality behind each algebra step.

Standard: G-CO.C.10

Words to know

rung: One line of the proof: a statement with its reason beside it.

Given / Prove: Given: the facts we start with. Prove: the statement the last rung must reach.

converse: The if-then turned around; it is a different statement, true or not.

base angles theorem: In a triangle with two congruent sides, the angles opposite them are congruent.

exterior angle: The angle outside a triangle, made by extending one side.

median: A segment from a corner to the midpoint of the opposite side.

midsegment: A segment joining the midpoints of two sides of a triangle.

parallel postulate: Through a point off a line, exactly one line is parallel to it.

Common mistakes

Your child named the converse of a theorem when the theorem itself was needed, for example the base angles theorem (equal sides give equal angles).

Your child wrote "Given" for the statement the proof is trying to reach. Only the facts on the Given line are given. Cover the Prove line and ask what is known.

Your child swapped two definitions: a median is a segment from a corner to the midpoint of the opposite side, and a midpoint splits a side into two equal halves. Draw a triangle and mark both.

What to say

Ask: which fact do we already have, the sides or the angles?

Questions parents ask

What is the most common mistake with triangle proofs: fill in the missing step or reason?

Your child named the converse of a theorem when the theorem itself was needed, for example the base angles theorem (equal sides give equal angles).

How can I help my child with triangle proofs: fill in the missing step or reason?

Ask: which fact do we already have, the sides or the angles?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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