Similarity proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Building Confidence

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. 1.

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

   • Given
   • ASA
   • SSS similarity theorem
   • AA similarity postulate
3. 2.

   Esme sews a small triangle SGH into the top of a sail SWY. Which reason fills the blank?

   • SAS similarity theorem
   • Given
   • AA similarity postulate
   • SAS
4. 3.

   Kira draws a beam SY across a roof GUW, level with the base UW. Which reason fills the blank?

   • Cross products property
   • Given
   • Triangle proportionality theorem
   • Converse of the triangle proportionality theorem
5. 4.

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

   • Triangle proportionality theorem
   • Given
   • Midsegment theorem
   • Converse of the triangle proportionality theorem
6. 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
   • Converse of the triangle proportionality theorem
   • Corresponding angles postulate

7. 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 -- ?.

8. 6.

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

   • Given
   • AA similarity postulate
   • Triangle proportionality theorem
   • AAS
9. 7.

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

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

10. 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.

11. 8.

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

    • ∠SHG ≅ ∠SWY
    • ∠SHG ≅ ∠SYW
    • △SGH ~ △SWY
    • ∠SHG ≅ ∠GSH
12. 9.

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

    • QC/QD = CF/FH
    • QC · FH = CD · QF
    • QC/CD = QF/FH
    • QC/CD = HF/QF
13. 10.

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

    • GS/GU = SY/YW
    • GS/SU = GY/YW
    • GS/SU = YW/GY
    • GS · YW = SU · GY