Introduction To Congruent Triangles

Congruent Triangles Introduction Two triangles are said to be congruent if a correspondence exists between them due to which all six parts of them, three sides and three angles of each, have equal measures. In simple words, two triangles are said to be congruent if and only if one of them can be made to superpose on the other so as to cover it exactly. Conversely, the other triangle should also superpose the first triangle. Let there be two triangles Triangle ABC and Triangle DEF . If Triangle ABC be superposed on Triangle DEF to cover it exactly and vice versa, then A falls on D, B falls on E and C falls on F.

Therefore AB = DE , BC = EF and AC = DF Moreover, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F . So we write Triangle ABC ≅ Triangle DEF It should be noted carefully that the order of the letters is very important. For example, if Triangle PQR ≅ Triangle STU , it means

∠P = ∠S , ∠Q = ∠T and ∠R = ∠U ; PQ=ST, QR=TU and RP=US

But if Triangle PQR ≅ Triangle STU and without caring for the order of letters, we write Triangle PQR ≅ TriangleTSU , and then this order stands for:

∠P = ∠T , ∠Q = ∠S and ∠R = ∠U ; PQ=TS, QR=SU and RP=UT All the above six relations are not true. Therefore, order of the alphabetical letters is very important.

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