Are these triangles similar? (angle-angle)

Answer Key - Grade 8 Math Worksheet

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

1. 1.

   Tala compares two mainsails, A and B. Are the two triangles similar?

   • Yes: both have the angles 38°, 67° and 75°, so they are similar
   • No: A's angles are 38° and 67° but B's are 38° and 75°, so they are not similar
   • Not enough to tell: we need the side lengths first
2. 2.

   Zee compares two tent flaps, A and B. Are the two triangles similar?

   • Not enough to tell: we need the side lengths first
   • No: A's angles are 44° and 56° but B's are 56° and 80°, so they are not similar
   • Yes: both have the angles 44°, 56° and 80°, so they are similar
3. 3.

   Kira compares two kite wings, A and B. We only know that each has a 50° angle. Are the triangles similar?

   • Yes: they have an equal angle, so the two triangles are similar
   • No: one equal angle means they are not similar
   • Not enough to tell yet: we need a second pair of equal angles
4. 4.

   Luz compares two paper triangles, A and B. We only know that each has a 90° angle. Are the triangles similar?

   • Not enough to tell yet: we need a second pair of equal angles
   • Yes: they share an equal angle, so the two triangles are similar
   • No: one equal angle means they are not similar
5. 5.

   Milo compares two tents, A and B. We only know that each has a 70° angle. Are the triangles similar?

   • Not enough to tell yet: we need a second pair of equal angles
   • Yes: they have one equal angle, so the two triangles are similar
   • No: one equal angle means they are not similar
6. 6.

   Noah compares two roofs, A and B. We only know that each has a 110° angle. Are the triangles similar?

   • No: one equal angle means they are not similar
   • Not enough to tell yet: we need a second pair of equal angles
   • Yes: they share one equal angle, so the two triangles are similar
7. 7.

   Pia cuts two right-triangle sails, A and B. How many cm long is B's side across the 37° angle?

   18
8. 8.

   Tala cuts two right-triangle roofs, A and B. How many cm long is B's side across the 28° angle?

   32
9. 9.

   Zee cuts two right-triangle tents, A and B. How many cm long is B's side across the 53° angle?

   36
10. 10.

    Ari cuts two right-triangle kite wings, A and B. How many cm long is B's side across the 53° angle?

    16