|Class 7 Maths Congruence of Triangles||Congruence of Triangles|
Congruence of Triangles
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure i.e. if they are copies of each other and when superposed, they cover each other exactly.
In the above figure, ΔABC and ΔPQR have the same size and shape. So, they are congruent. We can express this as ΔABC ≅ ΔPQR.
Thus, in these two congruent triangles, we have:
Corresponding vertices: A and P, B and Q, C and R.
Corresponding sides: AB and PQ, BC and QR, AC and PR.
Corresponding angles: ∠A and ∠P, ∠B and ∠Q, ∠C and ∠R.
Problem: If Δ DEF ≅ Δ BCA, write the part(s) of Δ BCA that correspond to:
(i) Ð E (ii) EF (iii) Ð F (iv) DF
Given: Δ DEF ≅ Δ BCA
(i) Ð E <-> Ð C
(ii) EF <-> CA
(iii) Ð F <-> Ð A
(iv) DF <-> BA