Question

write a true 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:

A conditional statement "if p then q" has a converse "if q then p". For an equilateral triangle (where all sides are equal), the converse of "if a triangle is equilateral then all its sides are equal" is "if all sides of a triangle are equal then it is equilateral", which is true. For a square (a four - sided polygon), the converse of "if a shape is a square then it is a four - sided polygon" is "if a shape is a four - sided polygon then it is a square", which is false as there are many non - square four - sided polygons. For an equilateral triangle, the converse of "if two sides of a triangle are equal then it is an equilateral triangle" is false since two equal sides make an isosceles triangle. For a triangle, the converse of "if two angles of a triangle are equal then two sides are equal" is the Isosceles Triangle Theorem converse, which is true.

Answer:

D. If two angles of a triangle are equal, then two sides of the triangle are equal.