Geo Un2Wk4 - Proof Writing Practice

Proving Statements about Segments and Angles

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​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

Open Ended

Why is the reason for the last question the substitution property?

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

Fill in the statement.

• 
  

  $$\angle2\ \cong\ \angle5$$

• $$m\angle2\ +\ m\angle5\ =\ 90$$
  

• $$m\angle2\ +\ m\angle5\ =\ 180$$
  

• < 2 and < 5 are a linear pair

Multiple Choice

Use the definition of a perpendicular bisector to complete the statement: "A perpendicular bisector of a segment is a line that is..."

• parallel to the segment.

• equal in length to the segment.

• perpendicular to the segment and bisects it.

• tangent to the segment.

Multiple Choice

Write a clear proof for the statement: "If two angles are supplementary and congruent, then each angle is $$90^\circ$$ ."

• Assume the angles are $$x$$ and $$y$$ . Since they are supplementary, $$x + y = 180^\circ$$ . Since they are congruent, $$x = y$$ . Therefore, $$2x = 180^\circ$$ , so $$x = 90^\circ$$ .

• Assume the angles are $$x$$ and $$y$$ . Since they are supplementary, $$x + y = 90^\circ$$ . Since they are congruent, $$x = y$$ . Therefore, $$2x = 90^\circ$$ , so $$x = 45^\circ$$ .

• Assume the angles are $$x$$ and $$y$$ . Since they are supplementary, $$x + y = 180^\circ$$ . Since they are congruent, $$x = y$$ . Therefore, $$2x = 180^\circ$$ , so $$x = 60^\circ$$ .

• Assume the angles are $$x$$ and $$y$$ . Since they are supplementary, $$x + y = 180^\circ$$ . Since they are congruent, $$x = y$$ . Therefore, $$2x = 180^\circ$$ , so $$x = 120^\circ$$ .