Similar shapes: matching sides and angles

Answer Key - Grade 7 Math Worksheet - Challenge Me

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

1. 1.

   One row 25 | 10 for the matching sides, with a box for the multiplier from A to B. Jun copies a big model door (A) into a small model (B), similar shapes. A is 25 cm tall and B is 10 cm tall. What is the scale factor from A to B?

   0.4
2. 2.

   One row 12 | 3 for the matching sides, with a box for the multiplier from A to B. Kira copies a kite design (A) onto a tiny sticker (B), similar shapes. A's tail is 12 cm and B's tail is 3 cm. What is the scale factor from A to B?

   0.25
3. 3.

   Noah compares two similar tent flaps. Triangle ABC is similar to triangle EFD. How many cm long is side FD?

   17.5
4. 4.

   Bo has similar roof triangles A and B. Every side of B is 2 times as long as A's. A has angles of 50° and 55°. How big is B's angle matching A's third angle?

   75
5. 5.

   Milo builds a small ramp (A) and a bigger, similar ramp (B), shown here. How many cm of tape go all the way around B's edge?

   47.5
6. 6.

   Noah orders a bigger print of a drawing. The drawing (A) is 4 by 6 inches and the print (B) is 6 by 9 inches. Are A and B similar?

   • Yes: both rectangles are longer than they are wide
   • No: the print is a different size than the drawing
   • No: the short sides differ by 2 inches but the long sides differ by 3
   • Yes: both pairs of sides are × 3/2
7. 7.

   Pia compares two windows. Window A is 4 by 6 feet and window B is 8 by 10 feet, with one curious bee on the glass. Are A and B similar?

   • No: 8 ÷ 4 = 2, but 10 ÷ 6 is not 2
   • Yes: both sides are 4 feet longer
   • Yes: the short side doubled, 4 feet to 8 feet
   • No: window B is bigger than window A
8. 8.

   Ren compares two tabletops. Table A is 12 by 20 dm and table B is 15 by 25 dm. Are A and B similar?

   • No: the short sides differ by 3 dm but the long sides differ by 5 dm
   • Yes: both rectangles are longer than they are wide
   • Yes: both pairs of sides are × 5/4
   • No: the two tabletops are different sizes
9. 9.

   Esme labels two similar roofs. Triangle LMN is similar to triangle STU. Angle M is 30°. Which corner of triangle STU has a 30° angle?

   • corner U
   • corner T
   • corner S
10. 10.

    One row 4 | 32 for the matching sides, with a box for the multiplier from B to A. Ari compares a model ramp (A) and a bigger ramp (B), similar triangles. A's base is 4 cm and B's base is 32 cm. What is the scale factor from B to A?

    0.125