Question

Which of these conditions might be true if polygons ABCD and KLMN are similar?

A.The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.

B.The measures of corresponding angles of ABCD and KLMN are in the ratio 1 : 2, but the lengths of corresponding sides of ABCD and KLMN are not proportional.

C.The lengths of corresponding sides of ABCD and KLMN are equal, but the measures of corresponding angles of ABCD and KLMN are not equal.

D.The lengths of corresponding sides of ABCD and KLMN are proportional, but the measures of corresponding angles of ABCD and KLMN are not equal.

E.The measures of corresponding angles of ABCD and KLMN are not proportional, but the lengths of corresponding sides of ABCD and KLMN are proportional.

Answer 1

I would say B.The measures of corresponding angles of ABCD and KLMN are in the ratio 1 : 2, but the lengths of corresponding sides of ABCD and KLMN are not proportional.

Answer 2

Option A is right

Explanation:

For any two geometrical figures to be similar we must have either the sides are in proportion or all angles are congruent.

If angles are not congruent then the two polygons cannot be similar. So option B which says angles are in the ratio 1:2 is incorrect.

If sides are equal, the two polygons need not be similar, example, a square and a rhombus. Hence option C is wrong

If sides are proportional and angles are not congruent then similarity cannot be there. Hence incorrect option d

Only correct answer is

Option a) The measures of corresponding angles of ABCD and KLMN are equal, but the lengths of corresponding sides of ABCD are half those of KLMN.