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Congruence

Congruence. Figures that have the same shape and size are said to be congruent . For example,. Congruent Triangles. Two triangles are congruent if all their conrresponding sides and angles are equal. For Example,. Conditions for Triangles to be Congruent.

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Congruence

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  1. Congruence Figures that have the same shape and size are said to be congruent. For example,

  2. Congruent Triangles Two triangles are congruent if all their conrresponding sides and angles are equal. For Example,

  3. Conditions for Triangles to be Congruent However, in certain cases, knowing that three pairs of corresponding parts are equal is sufficient to conclude that two triangles are congruent. If two triangles are congruent, there are six paires of corresponding parts which are equal.

  4. A X B C Y Z Case I (SSS) : Two triangles are congruent if all their corresponding sides are equal.

  5. A X B C Y Z Case II (SAS) : If two sides and the included angle of one triangle are to the corresponding parts of another triangle, the two triangles are congruent.

  6. A X B C Y Z Case IIIa (ASA) : If two angles and the included side of one triangle are equal to the corresponding parts of another triangle, the two triangles are congruent.

  7. A X B C Y Z Case IIIb (AAS) : If two angles and any side of one triangle are equal to the corresponding parts of another triangle, the two triangles are also congruent.

  8. A X B C Y Z Case IV (RHS) : If the hypotenuese and one side of a right-angled triangle are equal to the corresponding parts of another right-angled triangle, the two triangles are also congruent.

  9. Here are some examples to examine what you have learnt. In each of the following, tell whether the given pair of triangles are congruent or not. For each pair of congruent triangles, choose the correct condition:

  10. 1. Are they congruent ? Pls click on your answer No Yes, why ? SSS SAS ASA AAS RHS

  11. 2. Are they congruent ? Pls click on your answer No Yes, why ? SSS SAS ASA AAS RHS

  12. 3. Are they congruent ? Pls click on your answer No Yes, why ? SSS SAS ASA AAS RHS

  13. 4. Are they congruent ? Pls click on your answer No Yes, why ? SSS SAS ASA AAS RHS

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