Eric Nicholas K's answer to Kathy's Secondary 4 E Maths Singapore question.
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There are four ways to prove for congruency of two triangles.
1. All three corresponding sides are the same (Side - Side - Side / SSS property).
2. Two corresponding sides AND their included angle are equal (Side - Angle - Side / SAS property).
3. One corresponding side and ANY two included angles are equal (Angle - Side - Angle / ASA property).
4. [Special case, exclusive to right angled triangles] One right angle, the hypotenuse and one corresponding side are equal (Right Angle - Hypotenuse - Side / RHS property).
Note, however, that right-angled triangles can be proved by ANY of the four properties.
1. All three corresponding sides are the same (Side - Side - Side / SSS property).
2. Two corresponding sides AND their included angle are equal (Side - Angle - Side / SAS property).
3. One corresponding side and ANY two included angles are equal (Angle - Side - Angle / ASA property).
4. [Special case, exclusive to right angled triangles] One right angle, the hypotenuse and one corresponding side are equal (Right Angle - Hypotenuse - Side / RHS property).
Note, however, that right-angled triangles can be proved by ANY of the four properties.
Date Posted:
5 years ago
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