The contrapositive of the statement "If a shape is a square, then it has four equal sides" is:a.If a shape is not a square, then it does not have four equal sides.b.If a shape has four equal sides, then it is a square.c.If a shape does not have four equal sides, then it is not a square.d.If a shape is a square, then it has unequal sides.
Question
The contrapositive of the statement "If a shape is a square, then it has four equal sides" is:a.If a shape is not a square, then it does not have four equal sides.b.If a shape has four equal sides, then it is a square.c.If a shape does not have four equal sides, then it is not a square.d.If a shape is a square, then it has unequal sides.
Solution 1
The contrapositive of a statement is formed by negating both the hypothesis and the conclusion, and then swapping them. So, the contrapositive of the statement "If a shape is a square, then it has four equal sides" is: "If a shape does not have four equal sides, then it is not a square." Therefore, the correct answer is c. If a shape does not have four equal sides, then it is not a square.
Solution 2
To find the contrapositive of the statement "If a shape is a square, then it has four equal sides," we need to negate both the hypothesis and the conclusion and then switch their positions.
The hypothesis of the original statement is "a shape is a square," and its conclusion is "it has four equal sides."
To negate the hypothesis, we say "a shape is not a square." To negate the conclusion, we say "it does not have four equal sides."
Switching their positions, we get the contrapositive statement: "If a shape does not have four equal sides, then it is not a square."
Therefore, the correct answer is option c: "If a shape does not have four equal sides, then it is not a square."
Similar Questions
If all squares are rectangles, and all rectangles have four sides, which of the following statements is true?*1 pointSome squares are not rectangles.All rectangles are squares.All squares have four sides.All rectangles have four equal sides.
Try AgainOne of your answers is incorrect.True or False?Every parallelogram is a rectangle. TrueFalseEvery rectangle with four congruent sides is a square. TrueFalseEvery square is a rectangle. TrueFalseEvery quadrilateral is a square. TrueFalse
Every rectangle is a square. TrueFalseEvery rectangle with four congruent sides is a square. TrueFalseEvery rhombus is a rectangle. TrueFalseEvery quadrilateral is a square.
Select three true statements.ResponsesA A rhombus is always a square.A rhombus is always a square.B A square is always a rectangle.A square is always a rectangle.C A rectangle is always a square.A rectangle is always a square.D A square is always a rhombus.A square is always a rhombus.E A square is always a parallelogram.
State whether True or False.(a) All rectangles are squares. (b) All rhombuses are parallelograms.(c) All squares are rhombuses and also rectangles. (d) All squares are not parallelograms.(e) All kites are rhombuses. (f) All rhombuses are kites.(g) All parallelograms are trapeziums. (h) All squares are trapeziums.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.