To explain:
The following statement is true or false, gives its converse, inverse and contra-positive:
‘If a quadrilateral is a square, then it is a rectangle.’
Answer to Problem 47HP
The given statement is true.
Explanation of Solution
Given information:
The given statement is:
‘If a quadrilateral is a square, then it is a rectangle.’
Know that: A rectangle is quadrilateral which has four right
A square is both a rhombus and rectangle.
Therefore, a square is always rectangle.
Hence, the given statement is true.
- Converse: A quadrilateral is square when a quadrilateral is rectangle.
This is false statement. A rectangle is quadrilateral which has four right angles. It is not necessarily defined as rhombus therefore it is not necessarily a square.
- Inverse: A quadrilateral is not a rectangle when a quadrilateral is not square.
This is false statement. A rectangle is quadrilateral which has four right angles and two pairs of side are congruent. It is not necessarily defined as square.
- Contra positive: A quadrilateral is not a square, when a quadrilateral is not rectangle.
This is true statement. A rectangle is quadrilateral which has four right angles. A square is both a rhombus and rectangle. Therefore, a square is always rectangle.
Chapter 6 Solutions
Geometry, Student Edition
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