Are these triangles similar? (angle-angle)

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Noah compares two right-triangle paper corners, A and B. A has a 40° angle and B has a 45° angle. Are the triangles similar?

   • Yes: both have a right angle, so they are similar
   • Not enough to tell: we need the side lengths first
   • No: A's angles are 40°, 50° and 90° but B's are 45°, 45° and 90°, so they are not similar
2. 2.

   Pia compares two right-triangle signs, A and B. A has a 62° angle and B has a 28° angle. Are the triangles similar?

   • Not enough to tell: we need the side lengths first
   • No: A has a 62° angle but B has a 28° angle, so they are not similar
   • Yes: both have the angles 28°, 62° and 90°, so they are similar
3. 3.

   Tala labels the corners of two similar triangle warning signs. Which statement is true?

   • triangle CDF is similar to triangle WVU
   • triangle CDF is similar to triangle VWU
   • triangle CDF is similar to triangle UVW
4. 4.

   Zee labels the corners of two similar tent flaps. Which statement is true?

   • triangle GHQ is similar to triangle SUY
   • triangle GHQ is similar to triangle YSU
   • triangle GHQ is similar to triangle UYS

5. Read this first

   Use this

   (sketches, not to scale)

6. 5.

   Jun sorts three pairs of paper triangles by two angles each. Exactly one pair is similar. Which pair is it?

   • Pair 2
   • Pair 1
   • Pair 3
7. 6.

   Kira sorts three pairs of paper triangles by two angles each. Exactly one pair is similar. Which pair is it?

   • Pair 3
   • Pair 2
   • Pair 1
8. 7.

   Milo draws two right-triangle ramps, A and B. B has a 37° angle. How many cm long is B's side across the right angle?

   45
9. 8.

   Pia draws two right-triangle sails, A and B. B has a 23° angle. How many cm long is B's side across the right angle?

   65
10. 9.

    Ren draws two right-triangle kite wings, A and B. B has a 28° angle. How many cm long is B's side across the right angle?

    34
11. 10.

    Ari says two triangles are similar when two angles match. Triangles A and B both have a 46° angle and a 64° angle. Why must their third angles match too?

    • Each third angle is the same as the first angle, 46°
    • Each third angle is 46° + 64° = 110°
    • Each third angle is 360° − 46° − 64° = 250°
    • Each third angle is 180° − 46° − 64° = 70°