Geometry Logical Reasoning

2 lines that intersect to form a right angle

• Perpendicular Lines

• Intersecting Lines

• Parallel Lines

• Right Angle

A process that uses facts, definitions, accepted properties, and the laws of logic to form a logical argument

• Deductive Reasoning

• Inductive Reasoning

• Conjecture

• Proof

A type of proof written as numbered statements and corresponding reasons that show an argument in a logical order

• Two-Column Proof

• Converse

• Inverse

• Theorem

If angles are congruent, then the measures of the angles are equal. Identify the contrapositive.

• If the measures of the angles are equal, then the angles are congruent.

• If angles are not congruent, then the measures of the angles are not equal.

• If the measures of the angles are not equal, then the angles are not congruent.

• If the angles are not congruent, then the measure of the angles are equal.

Refer to the following statement: "If a polygon is a quadrilateral, then it is a trapezoid." What is the contrapositive 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.

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

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

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

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

• A rectangle is also a quadrilateral.

Which statement justifies that ∠1 ≅ ∠3?

• If two angles are vertical angles, then they are congruent.

• If two angles are a linear pair, then they are congruent.

• If two angles are congruent, then their measures are equal.

• If two parallel lines are cut by a transversal, then vertical angles are congruent.

Which statement justifies ∠3 and ∠6 are supplementary?

• If two angles are consecutive interior angles, then they are supplementary.

• If two angles are a linear pair, then they are supplementary.

• If two angles are supplementary, then their measures have a sum of 180.

• If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

Which statement justifies the conclusion made from the diagram?

• If a point is the midpoint of a segment, then it divides the segment into two congruent segments.

• If a point divides a segment into two congruent segments, then it is the midpoint of the segment.

• If AM = MB, then M is the midpoint of AB.

• If a point is in the middle of a segment, then it is the midpoint.

Name the property that is illustrated: If m∠A = m∠B and m∠B = m∠C, then m∠A = m∠C.

• Transitive Property of Equality

• Reflexive Property of Equality

• Symmetric Property of Equality

• Substitution Property of Equality