Geometric Theorems

Name the postulate, property, or theorem illustrated here.

• angle addition postulate

• addition property of equality

• addition

• segment addition postulate

Name the property, postulate, or theorem illustrated here.

• angle addition postulate

• addition property of equality

• addition

• segment addition postulate

If ∠A≅∠B and ∠B≅∠C, then ∠A≅∠C

• Reflexive Property of Congruence

• Transitive Property of Congruence

• Definition of Congruence

• Symmetric Property of Congruence

If ∠5 and ∠7 are vertical angles, then ∠5≅∠7

• Definition of Vertical Angles

• Vertical angle theorem (vertical angles are congruent)

• Definition of Congruence

• Definition of Supplementary

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 #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 reason justifies statement #2?

• Definition of Midpoint

• Transitive Property

• Addition Property

• Segment Addition Postulate

• Substitution Property

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