2.5 Proving Statements about Segments and Angles

2.5 Proving Statements about Segments and Angles

by Mary Lett

​Objective and Standards

• ​Students will be able to use a two-column proof to prove theorems about line segments and angles.

• ​HSG-CO.C.9: Prove theorems about lines and angles.

Vocabulary

• Proof: a logical argument that uses deductive reasoning to show that a statement is true.

• ​Two-Column Proof: has numbered statements and corresponding reasons that show an argument in a logical order.

Multiple Choice

Give the reason that belongs in the blank labeled 1.

• Given

• Substitution Property of Equality

• 4x = 20

• Division Property of Equality

Multiple Choice

Give the reason that belongs in the blank labeled 4.

• Given

• Substitution Property of Equality

• 4x = 20

• Division Property of Equality

Multiple Choice

Give the statement that belongs in the blank labeled 5.

• Given

• Substitution Property of Equality

• 4x = 20

• Division Property of Equality

Multiple Choice

Give the reason that belongs in the blank labeled 6.

• Given

• Substitution Property of Equality

• 4x = 20

• Division Property of Equality

​Vocabulary

• ​Theorem: a statement that can be proven.

  • ​Once you have proven a theorem, you can use it as a reason in other proofs.

Multiple Choice

Name the property that the statement illustrates.

• Reflexive Property of Segment Congruence

• Symmetric Property of Segment Congruence

• Transitive Property of Segment Congruence

• Reflexive Property of Angle Congruence

• Transitive Property of Angle Congruence

Multiple Choice

Name the property that the statement illustrates.

• Reflexive Property of Segment Congruence

• Symmetric Property of Segment Congruence

• Transitive Property of Segment Congruence

• Reflexive Property of Angle Congruence

• Transitive Property of Angle Congruence

​Proving the Symmetric Property of Segment Congruence

Multiple Choice

Which property justifies the next step?

• Symmetric Property
• Segment Addition Postulate
• Definition Midpoint
• Definition Congruence

Multiple Choice

Which property justifies the next step?

• Definition Congruence
• Segment Addition Postulate

• Transitive Property
• Definition Equality

Multiple Choice

If AB=CD then AB+EF = CD + EF

• Division property of equality
• Addition Property of equalilty
• Transitive property of equality
• Substitution property of equality

Multiple Choice

JK equals LM, then line segment JK is congruent to line segment LM

• Definition of midpoint
• Transitive Property of Segment Congruence

• Symmetric Property of Segment Congruence

• Definition of Congruence

Multiple Choice

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

• Transitive property of Equality

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

Multiple Choice

If Q is between P and R, then PQ +QR=PR

• Segment Addition postulate
• Definition of Midpoint
• Addition Property of equality
• Transitive Property of Equality

Multiple Choice

Give the Reason #1

• Given

• Segment Addition Property

• Addition Property of Equality

• PQ + QR = PR

• Transitive Property of Equality