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.

   Esme compares two isosceles tent fronts, A and B. A's top angle is 40°. B's two base angles are 70° each. Are the triangles similar?

   • Not enough to tell: we need the side lengths first
   • Yes: both have the angles 40°, 70° and 70°, so they are similar
   • No: A has a 40° angle but B has a 70° angle, so they are not similar
2. 2.

   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
3. 3.

   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?

   • Yes: both are isosceles triangles, so they are 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
4. 4.

   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?

   • Not enough to tell: we need the side lengths first
   • Yes: both have a right angle, so they are similar
   • No: A's angles are 40°, 50° and 90° but B's are 45°, 45° and 90°, so they are not similar
5. 5.

   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 UYS
   • triangle GHQ is similar to triangle YSU
6. 6.

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

   • triangle VWY is similar to triangle CDF
   • triangle VWY is similar to triangle FCD
   • triangle VWY is similar to triangle DFC
7. 7.

   “(sketches, not to scale)” Jun 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. 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.

   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 the same as the first angle, 33°
   • Each third angle is 33° + 52° = 85°
   • Each third angle is 180° − 33° − 52° = 95°
   • Each third angle is 360° − 33° − 52° = 275°
10. 10.

    Bo says two triangles are similar when two angles match. Triangles A and B both have a 58° angle and a 37° angle. Why must their third angles match too?

    • Each third angle is 180° − 58° − 37° = 85°
    • Each third angle is 360° − 58° − 37° = 265°
    • Each third angle is the same as the first angle, 58°
    • Each third angle is 58° + 37° = 95°