Segment Relationships

2.2 Segment Relationships

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The Ruler Postulate

Remember from lesson 2.1 that a postulate is something that we will accept to be true without proof. This postulate allows us to overlay a number line on any line segment so that we can use the corresponding numbers to quiclky assign a measure and to add or subtract distances.

Segment Addition Postulate

We discussed this postulate in action in the last unit. The basic idea here is that the whole really is the sum of its parts, nothing more and nothing less. We can add smaller segments to find the total length or subtract one part from a total length to find another part.

congruent:  this symbol means that are are talking about two things that are the same shape and the same size. 

We didn't look at section 2-6 of the book, but these three concepts, Reflexive, Symmetric, and transitive will come back again a number of time as we learn Geometry. More on each in the next slides...

This property is simply telling us that everything is congruent to itself (makes sense that everything is the same shape and same size as itself, right?)

This property tells us that congruencey is a two way street.  If one object is congruent to another, then the second is congruent to the first.  If you are the same age as your friend, then your friend is the same age as you. 

If two things are congruent to the same thing, then they are congruent to each other.  This is like saying Ray is wearing the same shirt as Sarah, and Fred is wearing the same shirt as Sarah, so we can say that Fred and Ray are wearing the same shirt. 

This is an example of a 2 column proof that uses the definition of congruence, the segment addition postulate, and substitution.

Multiple Choice

What property justifies this statement?

• Substitution Property

• Transitive Property

• Reflexive Property

• Symmetric Property

• None

Multiple Choice

What is reason 5?

• Transitive Property
• Reflexive Property
• Symmetric Property
• Prove

Multiple Choice

What is reason 4?

• Addition Property of Equality
• Subtraction Property of Equality
• Multiplication Property of Equality
• Division Property of Equality

Multiple Choice

What is reason 3?

• Addition Property of Equality
• Subtraction Property of Equality
• Multiplication Property of Equality
• Division Property of Equality

Multiple Choice

What is reason 2?

• Given
• Addition Property of Equality
• Subtraction Property of Equality
• Substitution Property of Equality

Multiple Choice

What is reason 1?

• Subtraction Property of Equality
• Transitive Property of Equality
• Given
• Prove

Multiple Choice

AB + BC = AC is justified by which option below?

• Angle Addition Postulate

• Addition Property

• Segment Addition Postulate

• Theorem 22C

Multiple Choice

Name the property described:
If MN = OP and OP = QR, then MN = QR

• Reflexive
• Symmetric
• Transitive
• Addition

Multiple Choice

Name the property described:
If PQ = RS then RS = PQ

• Reflexive
• Symmetric
• Transitive
• Addition

Multiple Choice

For any numbers a and b, if a = b, then b = a.

• Transitive Property         
• Reflexive Property 
• Symmetric Property   
• Substitution Property

Multiple Choice

If G is between S and B, write the segment addition equation you would use to solve for a length.

• BS+SG=BG

• SG+GB=SB

• SB+GB=SG

• BG+SG=SB

Multiple Choice

This point divides a line segment into 2 equal parts.

• point
• vertex
• midpoint
• segment

Multiple Choice

Name the property, definition, postulate, or theorem.

• def of congruent segments
• def of midpoint
• Segment Add Post
• def of angle bisector

Multiple Choice

Which property justifies the next step?

• Definition Congruence
• Segment Addition Post
• Transitive Property
• Definition Equality

Multiple Choice

Which property justifies the next step?

• Symmetric Property

• Transitive Property

• Segment Addition Property

• Reflexive Property

Multiple Choice

Which property justifies the next step?

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