If two geometrical figures have exactly the same shape and size then they are called congruent figures.
Note: (i) Two line segments are congruent only when their lengths are equal.
(ii) Two angles are congruent only when their degree measures are equal. ∠ABC ≌ ∠PQR
(iii) The symbol ‘≌’ is used to represent congruence.
Two triangles are congruent if and only if one of them can be made to superimpose on the other, such as to cover it exactly.
In the figure, ΔABC ≌ ΔDEF.
Note: (i) When ΔABC ≌ ΔDEF, then sides of ΔDEF fall on corresponding equal sides of ΔABC, i.e.
DE covers AB or DE ↔ AB; EF covers BC or EF ↔ BC and FD covers CA or FD ↔ CA.
(ii) In case ΔABC ≌ ΔDEF,
∠D covers ∠A or ∠D ↔ ∠A.
∠E covers ∠B or ∠E ↔ ∠B.
∠F covers ∠C or ∠F ↔ ∠C.
(iii) In case ΔABC ≌ ΔDEF
D corresponds to A or D ↔ A.
E corresponds to B or E ↔ B.
F corresponds to C or F ↔ C.
(iv) In congruent triangles, corresponding parts are equal and we write in short ‘c.p.c.t.’ “for Corresponding Parts of Congruent Triangles”.
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1. What are the properties of congruent triangles? |
2. How can you prove that two triangles are congruent? |
3. What is the significance of congruent triangles in geometry? |
4. How do congruent figures contribute to problem-solving in mathematics? |
5. Are congruent triangles and similar triangles the same thing? |
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