Reasoning and proof Knowledge-Based Download PDF

Questions

1. 1.

   Which property of equality justifies the statement: 'If $AB = CD$, then $CD = AB$'?

   • A) Symmetric Property of Equality
   • B) Reflexive Property of Equality
   • C) Transitive Property of Equality
   • D) Substitution Property of Equality
2. 2.

   Given the true conditional statement "If two angles form a linear pair, then they are supplementary" and the given fact that $\angle 1$ and $\angle 2$ form a linear pair, which conclusion follows by the Law of Detachment?

   • A) $\angle 1 \cong \angle 2$
   • B) If $\angle 1$ and $\angle 2$ are supplementary, then they form a linear pair.
   • C) $\angle 1$ and $\angle 2$ are supplementary.
   • D) The sum of the measures of $\angle 1$ and $\angle 2$ is equal to 90°.
3. 3.

   Which figure provides a valid counterexample to the conjecture: “If a quadrilateral has four congruent sides, then it is a square”?

   • A) A rectangle with adjacent sides of different lengths
   • B) An isosceles trapezoid with non-parallel congruent legs
   • C) A parallelogram with opposite sides congruent and unequal adjacent sides
   • D) A rhombus with non-perpendicular adjacent sides
4. 4.

   Consider the true conditional statements: "If two parallel lines are cut by a transversal, then alternate interior angles are congruent" and "If alternate interior angles are congruent, then their measures are equal." According to the Law of Syllogism, which conclusion must logically follow?

   • A) If two parallel lines are cut by a transversal, then the lines never intersect.
   • B) If the measures of alternate interior angles are equal, then two parallel lines are cut by a transversal.
   • C) If two parallel lines are cut by a transversal, then the measures of alternate interior angles are equal.
   • D) If two parallel lines are cut by a transversal, then alternate interior angles are supplementary.
5. 5.

   Consider the conditional statement: "If a quadrilateral is a rectangle, then its diagonals are congruent." Which statement represents the contrapositive of this conditional statement?

   • A) If the diagonals of a quadrilateral are congruent, then the quadrilateral is a rectangle.
   • B) If the diagonals of a quadrilateral are not congruent, then the quadrilateral is not a rectangle.
   • C) If a quadrilateral is not a rectangle, then its diagonals are not congruent.
   • D) A quadrilateral is a rectangle if and only if its diagonals are congruent.