Logic Statements and Proofs in Geometry

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid." What is a counterexample of this statement?

• If a polygon is a trapezoid, then it is a quadrilateral.

• If a polygon is not a quadrilateral, then it is not a trapezoid.

• If a polygon is not a trapezoid, then it is not a quadrilateral.

• A rectangle is also a quadrilateral.

What type of reasoning do we use when we write proofs?

• Inductive Reasoning

• Deductive Reasoning

• The Law of Syllogism

• The Law of Detachment

What is the term for a statement that is accepted as true without proof in geometry?

• Theorem

• Postulate

• Corollary

• Hypothesis

Which of the following is a logical argument used to prove geometric theorems?

• Inductive reasoning

• Deductive reasoning

• Intuitive reasoning

• Empirical reasoning

Which of the following statements is true about parallel lines?

• They intersect at one point.

• They never intersect.

• They intersect at two points.

• They are always perpendicular.

In the given proof, what is the statement for step 2?

Given: ∠1 and ∠3 are vertical angles. What should you conclude by the vertical angles theorem?

• undefined andundefined are right angles.

In the given proof, what are the reasons for step 1 and 2?

• Angles that form a linear pair are supplementary.

• Substitution

• Reflexive Property of Congruence

• Angles of equal measure are congruent.

In the given proof, what is the reason for step 1?

• Angles that form a linear pair are supplementary.

• Angles of Equal Measure are Congruent

• Reflexive Property of Congruence

• Definition of a Perpendicular Bisector

In the given proof, what is the statement for step 2?