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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Congruence proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Ren checks whether two pizza slices CDF and GHQ match. Which reason fills the blank?

    • ASA
    • SSS
    • Given
    • SAS

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

    • ASA
    • Given
    • SAS
    • AAS

  3. Zee checks whether two triangle signs CDF and GHQ match. Which reason fills the blank?

    • Given
    • SSS
    • ASA
    • AAS

  4. Ari checks whether two sandwich halves CDF and GHQ match. Which reason fills the blank?

    • SAS
    • SSS
    • HL
    • Given

  5. 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.

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

    • Given
    • Reflexive property
    • Symmetric property
    • CPCTC

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

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

  8. 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.

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

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

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

    • HY ≅ HY
    • HC ≅ HY
    • △HCY ≅ △HQY
    • CY ≅ HQ

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

    • GW ≅ DS
    • DW ≅ DW
    • DG ≅ DW
    • △DGW ≅ △DSW

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

    • DC ≅ YC
    • ∠DWC ≅ ∠YWC
    • ∠DWC ≅ ∠WDC
    • △WDC ≅ △WYC
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10th grade Congruence proofs: fill in the missing step or reason worksheet – printable
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About this worksheet

Congruence 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 choose the congruence rule (SSS, SAS, ASA, AAS, HL) that the rungs above support.
  • I can name where each pair of parts comes from: Given, a definition, the reflexive property or a theorem.
  • I can use CPCTC only after the triangles are proved congruent.

Standard: G-SRT.B.5, 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.

SSS, SAS, ASA, AAS, HL: The congruence rules; S is a pair of sides, A a pair of angles.

included: Between: the angle between two sides, or the side between two angles.

hypotenuse: The side across from the right angle.

reflexive property: A part matches itself, like a shared side CF ≅ CF.

angle bisector: A ray that cuts an angle into two congruent angles.

Common mistakes

Your child named a congruence rule whose letters do not match the parts that are known. Count the pairs of sides (S) and angles (A) together, then say the rule.

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 mixed up ASA and AAS. In ASA the known side lies between the two known angles; in AAS it does not. Trace the side and see where it sits.

Questions parents ask

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

Your child named a congruence rule whose letters do not match the parts that are known. Count the pairs of sides (S) and angles (A) together, then say the rule.

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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