Properties of Triangle
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 we prove that two triangles are congruent? |
3. What is the significance of the congruence criteria in solving triangle problems? |
4. Can two triangles be congruent if they have the same angles but different side lengths? |
5. What are some real-life applications of congruent triangles? |
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