Triangle proofs: fill in the missing step or reason

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   Kira draws a house roof SUW whose two slopes SU and SW are equal. Which reason fills the blank?

   • Converse of the base angles theorem
   • Base angles theorem
   • Definition of midpoint
   • Given
2. 2.

   Luz cuts a pizza slice CDF from tip C to point Q on the crust. Which reason fills the blank?

   • Definition of midpoint
   • Given
   • Definition of median
   • Midsegment theorem
3. 3.

   Milo sews a seam on a triangle sail HUV from corner H to point Y on the bottom edge. Which reason fills the blank?

   • Definition of median
   • Definition of midpoint
   • Given
   • Base angles theorem
4. 4.

   Noah draws a line on a pyramid face GSW from the top G to point Q on the base. Which reason fills the blank?

   • Definition of midpoint
   • Definition of median
   • Segment addition postulate
   • Given
5. 5.

   Ren measures a triangle road sign QDH and finds its two bottom angles equal. Which reason fills the blank?

   • Converse of the base angles theorem
   • Base angles theorem
   • Given
   • Definition of isosceles triangle
6. 6.

   Tala checks a ramp's side, triangle VCS, and finds its angles at C and S equal. Which reason fills the blank?

   • Given
   • Converse of the base angles theorem
   • Triangle angle sum theorem
   • Base angles theorem
7. 7.

   Zee cuts another pizza slice DGW from tip D to point Q on the crust. Which statement fills the blank?

   • GQ ≅ QW
   • Q is the midpoint of DG
   • DQ ⊥ GW
   • Q is the midpoint of GW
8. 8.

   Bo paints a stripe UV across a pyramid face CDF, joining the middles of two sides. Which statement fills the blank?

   • UV ≅ DF
   • UV ∥ DF
   • ∠CUV ≅ ∠CDF
   • CU ≅ CV
9. 9.

   Ari hangs a string inside tent front FCH from the top F to point S on the floor. Which statement fills the blank?

   • FS ⊥ CH
   • CS ≅ SH
   • S is the midpoint of CH
   • S is the midpoint of FC
10. 10.

    Esme sews a stripe GH across a triangle sail SWY, joining the middles of two sides. Which statement fills the blank?

    • SG ≅ SH
    • ∠SGH ≅ ∠SWY
    • GH ∥ WY
    • GH ≅ WY