Sure! Let's go through each statement one by one to determine which is false.
A. The sum of the measures of the angles of a quadrilateral is 180.
- This statement is False. The sum of the measures of the angles of a quadrilateral is actually 360 degrees, not 180 degrees. This is because a quadrilateral can be divided into two triangles, and the sum of the angles in each triangle is 180 degrees. Therefore, 180 degrees + 180 degrees = 360 degrees.
B. The base angles of an isosceles trapezoid are congruent.
- This statement is True. In an isosceles trapezoid, the non-parallel sides (the legs) are of equal length, and the base angles (the angles adjacent to each base) are congruent.
C. The diagonals of a parallelogram bisect each other.
- This statement is True. In a parallelogram, each diagonal bisects the other, meaning that they cut each other in half.
D. A square is a rectangle.
- This statement is True. A square is a special type of rectangle where all four sides are of equal length and all four angles are right angles.
From the above analysis, it is clear that statement A is the false one.
Therefore, the false statement is A.
