VJesus12 wrote:Is quadrilateral a square?
(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.
Target question: Is quadrilateral a square?
Statement 1: Three angles of a quadrilateral are 90 degrees each.
ASIDE: This also means that ALL FOUR angles are 90 degrees each.
This means that
EITHER the quadrilateral is a square OR the quadrilateral is a rectangle
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3 sides of a quadrilateral are equal in length.
There are many possible shapes that meet this condition.
For example,
the quadrilateral could be is a square OR the quadrilateral could be a rhombus
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Combining the statements, we get 4 90-degree angles, and at least 3 sides the same length.
This LOCKS the shape into a definite SQUARE
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
FOR REFERENCE
