Similar figures: corresponding sides, scale factor, and all circles are similar

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   Ari checks pairs of shapes by their side lengths, all in cm. Which pair is similar?

   • Triangles with sides 6, 8, 10 and 9, 12, 15
   • Right triangles with sides 3, 4, 5 and 5, 12, 13
   • Triangles with sides 3, 4, 5 and 6, 7, 8
   • Triangles with sides 4, 6, 8 and 6, 9, 11
2. 2.

   Bo checks pairs of shapes by their side lengths, all in cm. Which pair is similar?

   • Rectangles 5 by 7 and 8 by 10
   • Rectangles 3 by 5 and 6 by 8, with 90° angles
   • Rectangles 2 by 3 and 4 by 7
   • Rectangles 4 by 6 and 10 by 15
3. 3.

   Esme checks pairs of shapes by their side lengths, all in cm. Which pair is similar?

   • Isosceles triangles with sides 5, 5, 6 and 5, 5, 8
   • Triangles with sides 12, 5, 13 and 10, 26, 24
   • Triangles with sides 6, 9, 12 and 8, 12, 15
   • Triangles with sides 5, 7, 9 and 8, 10, 12
4. 4.

   Kira scales a boat drawing. △CDF ~ △UQS, with CD = 6, DF = 8, CF = 10 (cm). QS = 20 cm. What is the scale factor from △CDF to △UQS?

   5/2
5. 5.

   Luz scales a ramp drawing. △CDF ~ △SUQ, with CD = 4, DF = 6, CF = 8 (cm). SQ = 14 cm. What is the scale factor from △CDF to △SUQ?

   7/4
6. 6.

   Milo scales a star drawing. △UQS ~ △CDF, with UQ = 15, QS = 20, US = 25 (cm). DF = 8 cm. What is the scale factor from △UQS to △CDF?

   2/5
7. 7.

   Noah scales a park drawing. △CDF ~ △QSU, with CD = 9, DF = 12, CF = 15 (cm). SU = 20 cm. What is the scale factor from △CDF to △QSU?

   5/3
8. 8.

   Pia scales a house plan. △CDF ~ △UQS, with CD = 6 and DF = 10 in the first triangle. UQ = 15. How long is QS?

   25
9. 9.

   Ren scales a cheese plan. △CDF ~ △UQS, with CD = 4 and DF = 6 in the first triangle. UQ = 12. How long is QS?

   18
10. 10.

    Tala scales a pizza plan. △CDF ~ △UQS, with CD = 8 and DF = 12 in the first triangle. UQ = 6. How long is QS?

    9