1. The congruent triangles are:
- A and B: Congruent by ASA (Angle-Side-Angle). Both have angles of 60° and 50° with the included side of 8 cm.
- C and E: Congruent by ASA (Angle-Side-Angle). Both have angles of 35° and 70° with the included side of 6 cm.
- D and F: Congruent by SAS (Side-Angle-Side). Both have sides of 6 cm and 8 cm with the included angle of 40°.
2. Triangles ABC and DEF are congruent by AAS (Angle-Angle-Side).
- In triangle ABC, angle A is 70°, angle C is 50°, and side BC is 10 cm.
- In triangle DEF, angle E is 60°, angle F is 70°, and side DE is 10 cm.
- First, calculate the missing angle in each triangle:
- In triangle ABC, angle B = 180° - 70° - 50° = 60°.
- In triangle DEF, angle D = 180° - 60° - 70° = 50°.
- Now, we have:
- Angle A (70°) in ABC corresponds to angle F (70°) in DEF.
- Angle B (60°) in ABC corresponds to angle E (60°) in DEF.
- Side BC (10 cm) in ABC is opposite angle A and corresponds to side DE (10 cm) in DEF, which is opposite angle F.
- Since two angles and a non-included side are equal, the triangles are congruent by AAS.
Parent Tip: Review the logic above to help your child master the concept of congruence and triangles worksheet answers.
