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Grade 10 · Math · Geometry

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

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

  1. Read this first

    Use this

    Marked: matching arcs at U and D. Given: ∠CUV ≅ ∠CDF and ∠UCV ≅ ∠DCF. Prove: triangle CUV ~ triangle CDF. Ladder: 1. ∠CUV ≅ ∠CDF and ∠UCV ≅ ∠DCF -- Given; 2. triangle CUV ~ triangle CDF -- ?.

  2. Bo cuts a small triangle CUV off the tip of a pizza slice CDF. Which reason fills the blank?

    • Given
    • AA similarity postulate
    • ASA
    • SSS similarity theorem

  3. Jun ties a cord CF across a tent front QDH, level with the floor DH. Which reason fills the blank?

    • Midsegment theorem
    • Triangle proportionality theorem
    • Converse of the triangle proportionality theorem
    • Given

  4. Luz paints a stripe VQ across a road sign HCS that cuts its sides in the same ratio. Which reason fills the blank?

    • Given
    • Midsegment theorem
    • Triangle proportionality theorem
    • Converse of the triangle proportionality theorem

  5. Milo draws a line DW across a pyramid face YFG that cuts its sides in the same ratio. Which reason fills the blank?

    • Triangle proportionality theorem
    • Given
    • Corresponding angles postulate
    • Converse of the triangle proportionality theorem

  6. Use this

    Given: HU ∥ QC. Prove: triangle WHU ~ triangle WQC. Ladder: 1. HU ∥ QC -- Given; 2. ∠WHU ≅ ∠WQC -- Corresponding angles postulate; 3. ∠WUH ≅ ∠WCQ -- Corresponding angles postulate; 4. triangle WHU ~ triangle WQC -- ?.

  7. Noah cuts a small triangle WHU off a sandwich half WQC, cutting level with the edge QC. Which reason fills the blank?

    • SSS similarity theorem
    • AA similarity postulate
    • Given
    • ASA

  8. Use this

    Given: YG ∥ SV. Prove: triangle DYG ~ triangle DSV. Ladder: 1. YG ∥ SV -- Given; 2. ∠DYG ≅ ∠DSV -- Corresponding angles postulate; 3. ∠DGY ≅ ∠DVS -- Corresponding angles postulate; 4. triangle DYG ~ triangle DSV -- ?.

  9. Pia cuts a small triangle DYG off a pizza slice DSV, cutting level with the crust SV. Which reason fills the blank?

    • Given
    • Triangle proportionality theorem
    • AAS
    • AA similarity postulate

  10. Ren ties a cord UV across a tent front CDF, level with the floor DF. Which statement fills the blank?

    • ∠CUV ≅ ∠CDF
    • ∠CUV ≅ ∠CFD
    • ∠CUV ≅ ∠UVC
    • △CUV ~ △CDF

  11. Use this

    Given: GH ∥ WY. Prove: triangle SGH ~ triangle SWY. Ladder: 1. GH ∥ WY -- Given; 2. ∠SGH ≅ ∠SWY -- Corresponding angles postulate; 3. ? -- Corresponding angles postulate; 4. triangle SGH ~ triangle SWY -- AA similarity postulate.

  12. Tala sews a seam GH across a sail SWY, level with the bottom edge WY. Which statement fills the blank?

    • △SGH ~ △SWY
    • ∠SHG ≅ ∠GSH
    • ∠SHG ≅ ∠SWY
    • ∠SHG ≅ ∠SYW

  13. Zee draws a beam CF across a roof QDH, level with the base DH. Which statement fills the blank?

    • QC · FH = CD · QF
    • QC/CD = QF/FH
    • QC/QD = CF/FH
    • QC/CD = HF/QF

  14. Ari paints a stripe SY across a road sign GUW, level with the base UW. Which statement fills the blank?

    • GS · YW = SU · GY
    • GS/SU = GY/YW
    • GS/SU = YW/GY
    • GS/GU = SY/YW
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10th grade Similarity proofs: fill in the missing step or reason worksheet – printable
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About this worksheet

Similarity 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 with similar triangles.
  • I can tell a similarity rule from a congruence rule, and the triangle proportionality theorem from its converse.
  • I can follow the similar-triangles proof of the Pythagorean theorem.

Standard: G-SRT.B.4, G-SRT.B.5

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.

similar (~): Same shape, possibly a different size: matching angles congruent, sides in one ratio.

AA similarity postulate: Two pairs of congruent angles make two triangles similar.

triangle proportionality theorem: A line parallel to one side cuts the other two sides in the same ratio.

cross products property: If a/b = c/d, then ad = bc.

distributive property: a · b + c · b = b(a + c).

Common mistakes

Your child used a congruence rule (such as ASA) or said "congruent" for triangles that are only similar: the same shape at a different size. Similar triangles use AA, SAS or SSS similarity.

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 named the converse of the triangle proportionality theorem when the theorem itself was needed. The theorem goes from a parallel line to equal ratios; the converse goes back.

What to say

Ask: which fact do we have?

Questions parents ask

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

Your child used a congruence rule (such as ASA) or said "congruent" for triangles that are only similar: the same shape at a different size. Similar triangles use AA, SAS or SSS similarity.

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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