Geometry Reasoning and Proof

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?

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

• Alternate Exterior Angle are Congruent

• Reflexive Property of Congruence

• Angles that form a linear pair are supplementary.

• Alternate Interior Angles are Congruent.

Fill in the blanks to complete the geometric proof:

• ∠PQR = 38; B: Definition of Complementary Angles; C: Subtraction

  Property of Equality

• ∠PQR = 38; B: Definition of Supplementary Angles; C: Reflexive Property

• ∠PQR = 38; B: Definition of Vertical Angles; C: Transitive Property

• ∠PQR = 38; B: Definition of Complementary Angles; C: Substitution

How can you prove step #4?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

How can you prove step #2?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

What reason justifies statement #2?

• Definition of Midpoint

• Transitive Property

• Addition Property

• Segment Addition Postulate

• Substitution Property

How can you prove step #5?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

Identify the  missing statement or reason

• Given

• Vertical Angles Theorem

• Definition of Angle Bisector

• Alternate Interior Angles Theorem