Question

If two triangles are congruent, are they similar? Please explain why or why not.

Answer 1

Yes, they are similar.

Explanation:

For two triangles to be similar, it is sufficient if two angles of one triangle are equal to two angles of the other triangle. Note that if two angles of one are equal to two angles of the other triangle, the tird angles of the two triangles too will be equal.

If two triangles are congruent then all corresponding sides as well as corresponding angles of one triangle are equal to those of other triangles. This can happen in four cases

• one - when all sides of triangles are equal,
• two - if one side and two angles of one are equal to one side and two angles of other triangle.
• three - if two sides and included angle of one triangle are equal to two sides and included angle of other triangle
• four - if in two right angled triangles, one side and hypotenuse of one triangle are equal to one side and hypotenuse of other triangle.

Observe that for triangles to be similar, we just need all angles to be equal. But for triangles to be cogruent, angles as well as sides sholud be equal.

Hence, while congruent triangles are similar, similar triangles may not be congruent.