Question

if a conditional that has a false converse. choose the correct answer below. a. if a triangle has all sides equal, then it is an equilateral triangle. b. if a shape is a square, then it is a four - sided polygon. c. if two sides of a triangle are equal, then it is an equilateral triangle. d. if two angles of a triangle are equal, then two sides of the triangle are equal

Explanation:

Step1: Recall conditional - statement and converse rules

A conditional statement is of the form "if p, then q" and its converse is "if q, then p". A conditional statement can be true while its converse is false.

Step2: Analyze option A

The conditional statement "If a triangle has all sides equal, then it is an equilateral triangle" is true. Its converse "If a triangle is an equilateral triangle, then it has all sides equal" is also true.

Step3: Analyze option B

The conditional statement "If a shape is a square, then it is a four - sided polygon" is true. Its converse "If a shape is a four - sided polygon, then it is a square" is false since a four - sided polygon can be a rectangle, parallelogram etc.

Step4: Analyze option C

The conditional statement "If two sides of a triangle are equal, then it is an equilateral triangle" is false. An equilateral triangle has all three sides equal. Its converse "If a triangle is an equilateral triangle, then two sides of the triangle are equal" is true.

Step5: Analyze option D

The conditional statement "If two angles of a triangle are equal, then two sides of the triangle are equal" is the Isosceles - triangle theorem and is true. Its converse "If two sides of the triangle are equal, then two angles of the triangle are equal" is also true.

Answer:

B. If a shape is a square, then it is a four - sided polygon. Then its converse "If a shape is a four - sided polygon, then it is a square" is false.