Geometry Reasoning and Proof

Using the figure above, what is the reason for the following:
∠1 ≅ ∠3

• Vertical Angle Theorem
• Definition of Vertical Angles
• Congruent Angle Theorem
• Definition of Congruence

What is the reason for the  statements above?

• Definition of Congruence
• Symmetric Property of Congruence
• Reflexive Property of Equality
• Congruent Segments Theorem

What is the reason for the above?

• Angle Addition Postulate
• Segment Addition Postulate
• Definition of Midpoint
• Transitive Property of Congruence

What property is illustrated below?
a = b and b = c so a = c

• Reflexive Property of Equality
• Symmetric Property of Equality
• Transitive Property of Equality
• Substitution Property of Equality

What is the reason for the statements below?
Given: m∠1 + m∠2 = 90
Prove: ∠1 and ∠2 are complementary.

• Definition of Complementary Angles
• Congruent Complements Theorem
• Definition of Right Angles
• Angle Addition Postulate

What is the reason for the statement below?
Given: m∠1 = 63
m∠1 + m∠2 = 90
Prove: 63 + m∠2 = 90

• Reflexive Property of Equality
• Symmetric Property of Equality
• Transitive Property of Equality
• Substitution Property of Equality

What is the justification?

• Reflexive Prop.
• Symmetric Prop.
• Transitive Prop.
• Substitution

What is the justification?

• reflexive property
• definition of bisect
• definition of a midpoint
• substitution property

QR=QR

• Reflexive property of equality
• Symmetric property of equality
• Subtraction property of equality
• Transitive property of equality

If AB=BC and BC=CE then AB=CE

• Transitive property
• Multiplication of equality
• Reflective property of equality
• Distributive property of equality