Question

Draw two triangles of equal areas such that
a)they are congreunt by SSS

Answer 1

Answer:

(i) the triangles are congruent

△ABC≅△DEF

area(△ABC)=1×2+ ½ ×4=4sq. units

area(△DEF)=1×2+ ½ ×4=4sq. units

∴area(△ABC)=area(△DEF)

Thus, triangles are of equal areas and are congruent.

Perimeter:

As △ABC≅△DEF

By CPCT

AB=DE

BC=EF

AC=DF

Adding all the above 3, we get,

AB+BC+CA=DE+EF+FD

Perimeter of △ABC = Perimeter of △DEF

Thus, perimeters of congruent triangles are also equal.

(ii) the triangles are not congruent

△MNOnot≅△IJK

area(△MNO)=1×2+1×2=4sq. units

area(△IJK)=1×2+1×2=4sq. units

∴area(△MNO)=area(△IJK)

Thus, triangles are of equal areas and are congruent.

Perimeter:

Perimeter of △MNO = Perimeter of △IJK

Thus, perimeters of triangles are not equal.