Negate the following statements. In each case, determine which statement is true

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.

Explanation / Answer

a) First statement is True since intercepted arc for angle inscribed in semi circle is 180 and from inscribed angle theorem measure of that angle is half of intercepted arc so angle is 90 degree. Negation: Angle inscribed in semi circle is not right angled.

B) True:since triangle has only 3 sides ,3angles.

Negation: Every triangle has less than 3 sides.

C) False: Since we can construct rectangle whose all sides are not equal then it is not square.

Negation: Every rectangle is not square which is true.

4) False There are infinitely many points on line l.

Negation: There are not exactly three points on line.

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