Question

Provide a counterexample to the statement.

If the sums of the interior angles of two polygons are​ equal, then the polygons must be similar.

Answer 1

A counterexample to the statement that if the sums of the interior angles of two polygons are equal, then the polygons must be similar can be found by considering a rectangle and a parallelogram.

Step-by-step explanation:

A counterexample to the statement If the sums of the interior angles of two polygons are​ equal, then the polygons must be similar can be found by considering a rectangle and a parallelogram.

Both shapes have four sides and the sum of their interior angles is 360 degrees. However, they are not similar because their corresponding sides are not proportional.

Therefore, the statement is false and the counterexample of a rectangle and a parallelogram proves it.

Answer 2

acute triangle, obtuse triangle

Step-by-step explanation:

The sums of interior angles of all triangles are 180°, but the triangles are only similar if their corresponding angles are congruent.

An acute triangle and an obtuse triangle both have angle sums of 180°, but can never be similar to one another.