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.

   Ren compares two gable ends, A and B. Are the two triangles similar?

   • Not enough to tell: we need the side lengths first
   • Yes: both have the angles 36°, 64° and 80°, so they are similar
   • No: the first angles are 36° and 64°, so they are not similar
2. 2.

   Bo checks two triangle warning signs, A and B. Are the two triangles similar?

   • Not enough to tell: we need the side lengths first
   • Yes: both have a 48° angle, so they are similar
   • No: A's angles are 48°, 62° and 70° but B's are 48°, 57° and 75°, so they are not similar
3. 3.

   Esme compares two paper triangles, A and B. Are the two triangles similar?

   • Yes: both have a 35° angle, so they are similar
   • Not enough to tell: we need the side lengths first
   • No: A's angles are 35°, 65° and 80° but B's are 35°, 60° and 85°, so they are not similar
4. 4.

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

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

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

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

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

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

   Ren cuts two right-triangle ramps, A and B. How many cm long is B's side across the 23° angle?

   20
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.

    Bo cuts two right-triangle warning signs, A and B. How many cm long is B's side across the 67° angle?

    72