Proving and Using Geometric Properties

What is the missing step in constructing a perpendicular bisector of a line segment?

• Without changing the compasses' width, draw an arc only above the line.

• Without changing the compasses' width, draw an arc above and below the line.

• Without changing the compasses' width, draw an arc only below the line.

Which is the geometric mean for this triangle?

See diagram

• 1

• 2

• 3

• 4

How can you prove step #2?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

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

What is the "reason" for step 5 of the proof?

• Angle Bisector Theorem

• Reflexive property

• CPCTC Theorem

• Proof

How can you prove step #5?

• Vertical angle theorem

• Subtraction property of equality

• Transitive property of congruence

• Definition of supplementary angles

How can you prove step #4?

• 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