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?

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

   Jun compares two isosceles roofs, A and B. A's top angle is 50°. B's two base angles are 55° each. Are the triangles similar?

   • Yes: both are isosceles triangles, so they are similar
   • Not enough to tell: we need the side lengths first
   • No: A's angles are 50°, 65° and 65° but B's are 55°, 55° and 70°, so they are not similar
3. 3.

   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?

   • No: A has a 35° angle but B has a 110° angle, so they are not similar
   • Yes: both have the angles 35°, 35° and 110°, so they are similar
   • Not enough to tell: we need the side lengths first
4. 4.

   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
   • Not enough to tell: we need the side lengths first
   • No: A's angles are 50°, 50° and 80° but B's are 60°, 60° and 60°, so they are not similar
5. 5.

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

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

   “sketches, not to scale” Esme 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
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 1
   • Pair 3
   • Pair 2
8. 8.

   Milo draws two right-triangle ramps, A and B. B has a 37° angle. How many cm long is B's side across the right angle?

   45
9. 9.

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