Question

iii. state whether each pair of triangles is congruent by sss, sas, asa, aas, hl, or none.

Explanation:

Step1: Recall congruence criteria

SSS (Side - Side - Side): All three sides of one triangle are equal to the corresponding three sides of the other triangle. SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of the other triangle. ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to the corresponding two angles and included side of the other triangle. AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of the other triangle. HL (Hypotenuse - Leg) is for right - angled triangles where the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of the other right - angled triangle.

Step2: Analyze each pair

For each pair of triangles, identify the marked equal sides and angles. Match the given equal parts with the congruence criteria. For example, if three sides are marked equal in two triangles, it is SSS. If two sides and the angle between them are marked equal, it is SAS and so on.

1. HL (right - angled triangles with hypotenuse and one leg equal)
2. SAS (two sides and included angle equal)
3. ASA (two angles and included side equal)
4. AAS (two angles and non - included side equal)
5. SAS (two sides and included angle equal)
6. HL (right - angled triangles with hypotenuse and one leg equal)
7. SAS (two sides and included angle equal)
8. SSS (three sides equal)
9. SSS (three sides equal)
10. HL (right - angled triangles with hypotenuse and one leg equal)
11. ASA (two angles and included side equal)
12. AAS (two angles and non - included side equal)
13. HL (right - angled triangles with hypotenuse and one leg equal)
14. SAS (two sides and included angle equal)
15. SSS (three sides equal)
16. HL (right - angled triangles with hypotenuse and one leg equal)
17. ASA (two angles and included side equal)
18. ASA (two angles and included side equal)
19. AAS (two angles and non - included side equal)
20. AAS (two angles and non - included side equal)
21. HL (right - angled triangles with hypotenuse and one leg equal)
22. SSS (three sides equal)
23. HL (right - angled triangles with hypotenuse and one leg equal)
24. SAS (two sides and included angle equal)
25. AAS (two angles and non - included side equal)
26. AAS (two angles and non - included side equal)
27. AAS (two angles and non - included side equal)
28. HL (right - angled triangles with hypotenuse and one leg equal)
29. SSS (three sides equal)
30. SAS (two sides and included angle equal)

Answer:

1. HL
2. SAS
3. ASA
4. AAS
5. SAS
6. HL
7. SAS
8. SSS
9. SSS
10. HL
11. ASA
12. AAS
13. HL
14. SAS
15. SSS
16. HL
17. ASA
18. ASA
19. AAS
20. AAS
21. HL
22. SSS
23. HL
24. SAS
25. AAS
26. AAS
27. AAS
28. HL
29. SSS
30. SAS