Congruent Triangles Worksheets | KS3 Maths | Beyond - Twinkl - Free Printable
Educational worksheet: Congruent Triangles Worksheets | KS3 Maths | Beyond - Twinkl. Download and print for classroom or home learning activities.
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Step-by-step solution for: Congruent Triangles Worksheets | KS3 Maths | Beyond - Twinkl
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Show Answer Key & Explanations
Step-by-step solution for: Congruent Triangles Worksheets | KS3 Maths | Beyond - Twinkl
1. In the first triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 5 cm, so the hypotenuse is 10 cm, and the side opposite the 60° angle is 5√3 cm. The missing lengths are 10 cm and 5√3 cm.
2. In the second triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 7 cm, so the hypotenuse is 7√2 cm. The missing length is 7√2 cm.
3. In the third triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 8 cm, so the hypotenuse is 16 cm, and the side opposite the 60° angle is 8√3 cm. The missing lengths are 16 cm and 8√3 cm.
4. In the fourth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 6 cm, so the hypotenuse is 12 cm, and the side opposite the 60° angle is 6√3 cm. The missing lengths are 12 cm and 6√3 cm.
5. In the fifth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 10 cm, so the hypotenuse is 10√2 cm. The missing length is 10√2 cm.
6. In the sixth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 4 cm, so the hypotenuse is 8 cm, and the side opposite the 60° angle is 4√3 cm. The missing lengths are 8 cm and 4√3 cm.
7. In the seventh triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 12 cm, so the hypotenuse is 12√2 cm. The missing length is 12√2 cm.
8. In the eighth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 9 cm, so the hypotenuse is 18 cm, and the side opposite the 60° angle is 9√3 cm. The missing lengths are 18 cm and 9√3 cm.
9. In the ninth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 14 cm, so the hypotenuse is 14√2 cm. The missing length is 14√2 cm.
10. In the tenth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 11 cm, so the hypotenuse is 22 cm, and the side opposite the 60° angle is 11√3 cm. The missing lengths are 22 cm and 11√3 cm.
11. In the eleventh triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 16 cm, so the hypotenuse is 16√2 cm. The missing length is 16√2 cm.
12. In the twelfth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 13 cm, so the hypotenuse is 26 cm, and the side opposite the 60° angle is 13√3 cm. The missing lengths are 26 cm and 13√3 cm.
13. In the thirteenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 18 cm, so the hypotenuse is 18√2 cm. The missing length is 18√2 cm.
14. In the fourteenth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 15 cm, so the hypotenuse is 30 cm, and the side opposite the 60° angle is 15√3 cm. The missing lengths are 30 cm and 15√3 cm.
15. In the fifteenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 20 cm, so the hypotenuse is 20√2 cm. The missing length is 20√2 cm.
16. In the sixteenth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 17 cm, so the hypotenuse is 34 cm, and the side opposite the 60° angle is 17√3 cm. The missing lengths are 34 cm and 17√3 cm.
17. In the seventeenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 22 cm, so the hypotenuse is 22√2 cm. The missing length is 22√2 cm.
18. In the eighteenth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 19 cm, so the hypotenuse is 38 cm, and the side opposite the 60° angle is 19√3 cm. The missing lengths are 38 cm and 19√3 cm.
19. In the nineteenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 24 cm, so the hypotenuse is 24√2 cm. The missing length is 24√2 cm.
20. In the twentieth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 21 cm, so the hypotenuse is 42 cm, and the side opposite the 60° angle is 21√3 cm. The missing lengths are 42 cm and 21√3 cm.
2. In the second triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 7 cm, so the hypotenuse is 7√2 cm. The missing length is 7√2 cm.
3. In the third triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 8 cm, so the hypotenuse is 16 cm, and the side opposite the 60° angle is 8√3 cm. The missing lengths are 16 cm and 8√3 cm.
4. In the fourth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 6 cm, so the hypotenuse is 12 cm, and the side opposite the 60° angle is 6√3 cm. The missing lengths are 12 cm and 6√3 cm.
5. In the fifth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 10 cm, so the hypotenuse is 10√2 cm. The missing length is 10√2 cm.
6. In the sixth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 4 cm, so the hypotenuse is 8 cm, and the side opposite the 60° angle is 4√3 cm. The missing lengths are 8 cm and 4√3 cm.
7. In the seventh triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 12 cm, so the hypotenuse is 12√2 cm. The missing length is 12√2 cm.
8. In the eighth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 9 cm, so the hypotenuse is 18 cm, and the side opposite the 60° angle is 9√3 cm. The missing lengths are 18 cm and 9√3 cm.
9. In the ninth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 14 cm, so the hypotenuse is 14√2 cm. The missing length is 14√2 cm.
10. In the tenth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 11 cm, so the hypotenuse is 22 cm, and the side opposite the 60° angle is 11√3 cm. The missing lengths are 22 cm and 11√3 cm.
11. In the eleventh triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 16 cm, so the hypotenuse is 16√2 cm. The missing length is 16√2 cm.
12. In the twelfth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 13 cm, so the hypotenuse is 26 cm, and the side opposite the 60° angle is 13√3 cm. The missing lengths are 26 cm and 13√3 cm.
13. In the thirteenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 18 cm, so the hypotenuse is 18√2 cm. The missing length is 18√2 cm.
14. In the fourteenth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 15 cm, so the hypotenuse is 30 cm, and the side opposite the 60° angle is 15√3 cm. The missing lengths are 30 cm and 15√3 cm.
15. In the fifteenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 20 cm, so the hypotenuse is 20√2 cm. The missing length is 20√2 cm.
16. In the sixteenth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 17 cm, so the hypotenuse is 34 cm, and the side opposite the 60° angle is 17√3 cm. The missing lengths are 34 cm and 17√3 cm.
17. In the seventeenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 22 cm, so the hypotenuse is 22√2 cm. The missing length is 22√2 cm.
18. In the eighteenth triangle, the angles are 30° and 60°, so the third angle is 90°. This is a 30-60-90 triangle. The side opposite the 30° angle is 19 cm, so the hypotenuse is 38 cm, and the side opposite the 60° angle is 19√3 cm. The missing lengths are 38 cm and 19√3 cm.
19. In the nineteenth triangle, the angles are 45° and 45°, so the third angle is 90°. This is a 45-45-90 triangle. The side opposite the 45° angle is 24 cm, so the hypotenuse is 24√2 cm. The missing length is 24√2 cm.
20. In the twentieth triangle, the angles are 30° and 90°, so the third angle is 60°. This is a 30-60-90 triangle. The side opposite the 30° angle is 21 cm, so the hypotenuse is 42 cm, and the side opposite the 60° angle is 21√3 cm. The missing lengths are 42 cm and 21√3 cm.
Parent Tip: Review the logic above to help your child master the concept of additional congruence methods worksheet.
