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.

   Kira compares two isosceles sails, A and B. A's two base angles are 35° each. B's top angle is 110°. Are the triangles similar?

   • Not enough to tell: we need the side lengths first
   • Yes: both have the angles 35°, 35° and 110°, so they are similar
   • No: A has a 35° angle but B has a 110° angle, so they are not similar
2. 2.

   Luz compares two isosceles kite wings, A and B. A's top angle is 80°. B's two base angles are 60° each. Are the triangles similar?

   • No: A's angles are 50°, 50° and 80° but B's are 60°, 60° and 60°, so they are not similar
   • Not enough to tell: we need the side lengths first
   • Yes: both are isosceles triangles, so they are similar
3. 3.

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

   • triangle GHQ is similar to triangle UYS
   • triangle GHQ is similar to triangle YSU
   • triangle GHQ is similar to triangle SUY
4. 4.

   Ari labels the corners of two similar sails. Which statement is true?

   • triangle VWY is similar to triangle FCD
   • triangle VWY is similar to triangle CDF
   • triangle VWY is similar to triangle DFC
5. 5.

   Bo labels the corners of two similar kite wings. Which statement is true?

   • triangle DFG is similar to triangle SHQ
   • triangle DFG is similar to triangle HQS
   • triangle DFG is similar to triangle QSH
6. 6.

   “(sketches, not to scale)” Luz sorts three pairs of paper triangles by two angles each. Exactly one pair is similar. Which pair is it?

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

   Noah draws two right-triangle tent sides, A and B. B has a 53° angle. How many cm long is B's side across the right angle?

   40
8. 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
9. 9.

   Tala says two triangles are similar when two angles match. Triangles A and B both have a 54° angle and a 66° angle. Why must their third angles match too?

   • Each third angle is 180° − 54° − 66° = 60°
   • Each third angle is the same as the first angle, 54°
   • Each third angle is 54° + 66° = 120°
   • Each third angle is 360° − 54° − 66° = 240°
10. 10.

    Zee says two triangles are similar when two angles match. Triangles A and B both have a 33° angle and a 52° angle. Why must their third angles match too?

    • Each third angle is 33° + 52° = 85°
    • Each third angle is 360° − 33° − 52° = 275°
    • Each third angle is the same as the first angle, 33°
    • Each third angle is 180° − 33° − 52° = 95°