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.

   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
2. 2.

   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
3. 3.

   Milo compares two right-triangle ramps, A and B. A has a 35° angle and B has a 55° angle. Are the triangles similar?

   • Yes: both have the angles 35°, 55° and 90°, so they are similar
   • Not enough to tell: we need the side lengths first
   • No: A has a 35° angle but B has a 55° angle, so they are not similar
4. 4.

   Ren compares two right-triangle roof frames, A and B. A has a 20° angle and B has a 60° 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 20°, 70° and 90° but B's are 30°, 60° and 90°, so they are not similar
5. 5.

   Ari labels the corners of two similar sails. Which statement is true?

   • triangle VWY is similar to triangle CDF
   • triangle VWY is similar to triangle FCD
   • triangle VWY is similar to triangle DFC
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 1
   • Pair 3
   • Pair 2

7. Read this first

   Use this

   (sketches, not to scale)

8. 7.

   Kira 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
9. 8.

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

   • Pair 2
   • Pair 3
   • Pair 1
10. 9.

    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
11. 10.

    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