Geometry and Algebraic Proofs

What is the congruent complements theorem

• If angles are complementary to the same angle then those two angles are congruent

• If angles are complementary to the same angle then those two angles are congruent

• If angles are complementary to the same angle then those two angles are congruent

• If angles are complementary to the same angle then those two angles are congruent

What is a line segment?

• A geometric figure

• Part of a line with two endpoint

• A shared end point of the sides of a angle

• Two angles that are opposite of each other

What is the congruent supplements theorem? 

• If angles are complementary to the same angle then those two angles are congruent

• If S in the interior angle PQR then angle SQR = angle PQR

• If angles are supplementary to the same angle those two angles are congruent

• All right 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 #2?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

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

What reason justifies statement #2?

• Definition of Midpoint

• Transitive Property

• Addition Property

• Segment Addition Postulate

• Substitution Property

How can you prove step #4?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

The algebraic expression that gives the distance between two points on a coordinate plane.

• Line Segment

• Distance Formula

• Midpoint Formula

• Slope Formula