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.

   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
   • Not enough to tell: we need the side lengths first
   • Yes: both have the angles 35°, 35° and 110°, so they are similar
2. 2.

   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?

   • 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
   • Yes: both are isosceles triangles, so they are similar
3. 3.

   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?

   • Yes: both have a right angle, so they are similar
   • Not enough to tell: we need the side lengths first
   • No: A's angles are 40°, 50° and 90° but B's are 45°, 45° and 90°, so they are not similar
4. 4.

   “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 1
   • Pair 2
   • Pair 3

5. Read this first

   Use this

   (sketches, not to scale)

6. 5.

   Jun sorts three pairs of paper triangles by two angles each. Exactly one pair is similar. Which pair is it?

   • Pair 3
   • Pair 1
   • Pair 2
7. 6.

   Kira 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. 7.

   Noah draws two right-triangle tent sides, A and B. B has a 53° angle. How many cm long is B's side across the right angle?

   40
9. 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
10. 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 180° − 33° − 52° = 95°
    • Each third angle is 360° − 33° − 52° = 275°
    • Each third angle is the same as the first angle, 33°
    • Each third angle is 33° + 52° = 85°
11. 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 58° + 37° = 95°
    • Each third angle is 360° − 58° − 37° = 265°
    • Each third angle is the same as the first angle, 58°