Each of the following cases contains certain measurements taken from two triangles. Class 7

Each of the following cases contains certain measurements taken from two triangles. Class 7

Question 1.

Each of the following cases contains certain measurements taken from two triangles. Identify the pairs in which the triangles are congruent to each other, with reason. Express the congruence whenever they are congruent. Class 7

(a) AB = DE

BC = EF

CA = DF

Solution:

∆ABC ≅ ∆DEF (SSS condition)

(b) AB = EF

∠A = ∠E

AC = ED

Solution:

∆ABC ≅ ∆EFD (SAS condition)

(c) AB = DF

∠B = ∠D = 90°

AC = FE

Solution:

∆ABC ≅ ∆FDE (RHS condition)

(d) ∠A = ∠D

∠B = ∠E

AC = DF

Solution:

∆ABC ≅ ∆DEF (AAS condition)

(e) AB = DF

∠B = ∠F

AC = DE

Solution:

Not congruent.