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.

   One row 16 | 10 for the matching sides, with a box for the multiplier from A to B. Luz shrinks a tent model (A) into a mini tent (B), similar shapes. A's pole is 16 cm and B's matching pole is 10 cm. What is the scale factor from A to B?

   0.625
4. 4.

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

   17.5
5. 5.

   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
6. 6.

   Luz cuts a small sail (A) and a bigger, similar sail (B), shown here. How many cm of rope go all the way around B's edge?

   36
7. 7.

   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
8. 8.

   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?

   • No: the short sides differ by 2 inches but the long sides differ by 3
   • Yes: both pairs of sides are × 3/2
   • No: the print is a different size than the drawing
   • Yes: both rectangles are longer than they are wide
9. 9.

   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
   • No: window B is bigger than window A
   • Yes: both sides are 4 feet longer
   • Yes: the short side doubled, 4 feet to 8 feet
10. 10.

    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 S
    • corner T
    • corner U