Triangle similarity: AA, SSS and SAS

Answer Key - Grade 10 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Jun makes two triangle flags for a boat and wants △CDF ~ △QSU by SAS~. How long must QU be, in cm?

   15
2. 2.

   Kira plans two ramps for a toy car track and wants △GHY ~ △VWC by SAS~. How long must VC be, in cm?

   12
3. 3.

   Luz sketches a small and a big tent side and wants △QSU ~ △DFG by SAS~. How long must DG be, in cm?

   21
4. 4.

   Milo cuts two triangle sandwiches for a picnic and wants △VWY ~ △CDF by SAS~. How long must CF be, in cm?

   15
5. 5.

   Noah compares two triangle pizza slices, △CDF and △QSU. Which statement is true?

   • Similar by SSS~, scale factor 2/3
   • Similar by SSS~, scale factor 3/2
   • Not similar: the sides grow by 3, 4 and 5
   • Congruent by SSS
6. 6.

   Pia compares two cheese wedges with triangle faces, △CDF and △QSU. Which statement is true?

   • Not similar: 6/4 and 8/6 are different
   • Congruent by SSS
   • Similar by SSS~: every side is 2 longer
   • Similar by SSS~, scale factor 3/2
7. 7.

   Ren compares two kite halves, △CDF and △QSU. Which statement is true?

   • Congruent by SAS
   • Similar by SSS~
   • Not enough: the third sides are not given
   • Similar by SAS~
8. 8.

   Tala compares two tent doors, △CDF and △QSU. Which statement is true?

   • Not similar: 65° and 75° do not match
   • Not enough: side lengths are needed
   • Congruent by AA
   • Similar by AA: ∠F = 75° = ∠U
9. 9.

   Zee looks at a roof front with a beam GH across it. In △CDF, G is on CD, H is on CF, and GH ∥ DF. How long is DF, in feet?

   15
10. 10.

    Ari looks at a tent front with a crossbar GH. In △CDF, G is on CD, H is on CF, and GH ∥ DF. How long is DF, in feet?

    21