Geometry Reasoning and Proof

What is "given information" in a proof?

• Words or information from a picture/diagram that is given to the problem solver

• The answer

• The properties you use to write a proof.

• Answer not listed

Why are proofs necessary in geometry?

• Because we all love them

• To make this class harder

• Shows that you understand clear, logical thinking

Write the conditional statement as a biconditional statement: If two lines intersect at a 90 degree angle, then those two lines are perpendicular.

• Two lines intersect at a 90 degree angle if and only if they are perpendicular.

• If two lines do not intersect at a 90 degree angle, then the two lines are not perpendicular.

• If two lines intersect at a 90 degree angle if and only if then they are perpendicular.

• If two lines are perpendicular, then they intersect at a 90 degree angle.

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

• 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.

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

What is the missing reason in the proof?

• Addition

• Segment Addition Postulate

• Substitution

• Transitive Property

What is the missing statement in the proof?

• m∠ABD+m∠DBC=m∠ABC

• m∠ABD=m∠DBC

• m∠ABC=m∠ABC

• none of the other choices are correct

Which is the correct reason for statements 2 and 4 in the proof?

• Given

• Transitive Property

• Definition of Congruent Angles

• Vertical Angles are congruent.

What is the REASON for Statement #2?

• Given

• Definition of Complementary Angles

• Substitution Property

• Reflexive Property of Congruence

What is the REASON for Statement #3?

• Given

• Definition of Complementary Angles

• Substitution Property

• Reflexive Property of Congruence