Question

Negate the following statements. In each case, determine which statement is true, the original statement or its negation.

a) An angle inscribed in a semicircle is a right angle.

b) Every triangle has at least three sides.

c) Every rectangle is a square.

d) There are exactly three points on every line.

e) Through any two distinct points there is at least one line.

f) Every rectangle has three sides, and all right triangles are equilateral.

g) Triangle XYZ is isosceles, or a pentagon is a five-sided plane figure.

Answer 1

a) True.

Negation - An angle inscribed in a semicircle is not right angle.

b) False.

Negation - Every triangle has sides less than 3.

c) False.

Negation - Every rectangle is not a square.

d) False.

Negation - There are not exactly 3 points on a line.

e) True.

Negation - Through 2 points there is one and only one line.

f) False.

Negation - Every rectangle doesn't have 3 sides and all right triangles are not equilateral.

g) False.

Triangle XYZ is not isosceles or a Pentagon is not a five sided plane figure.