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.

   Pia compares two kite panels, A and B. Are the two triangles similar?

   • Not enough to tell: we need the side lengths first
   • No: the first angles are 41° and 59°, so the two kite panels are not similar
   • Yes: both have the angles 41°, 59° and 80°, so they are similar
2. 2.

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

   • Not enough to tell: we need the side lengths first
   • No: the first angles are 36° and 64°, so they are not similar
   • Yes: both have the angles 36°, 64° and 80°, so they are similar
3. 3.

   Tala compares two mainsails, A and B. Are the two triangles 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
   • Yes: both have the angles 38°, 67° and 75°, so they are similar
4. 4.

   Ari compares two ramp sides, A and B. Are the two triangles similar?

   • No: A's angles are 52° and 73° but B's are 55° and 52°, so they are not similar
   • Yes: both have the angles 52°, 55° and 73°, so they are similar
   • Not enough to tell: we need the side lengths first
5. 5.

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

   • Not enough to tell: we need the side lengths first
   • Yes: both have a 35° angle, so they are similar
   • No: A's angles are 35°, 65° and 80° but B's are 35°, 60° and 85°, so they are not similar
6. 6.

   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
   • Yes: they have an equal angle, so the two triangles are similar
   • No: one equal angle means they are not similar
7. 7.

   Luz compares two paper triangles, A and B. We only know that each has a 90° 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 an equal angle, so the two triangles are similar
8. 8.

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

   • Yes: they share one 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
9. 9.

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

   18
10. 10.

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

    32