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Segment proofs

Page history last edited by Piljung Yun 11 years, 2 months ago

___(0-10 pts) Describe the segment properties of

 

 congruence. Give at least 3 examples.

 

Symmetric Property of Congruence:

If segment AB is congruent to segment CD, then segment CD is congruent to segment AB. This is because both have the same measurements and can easily substitute each other.

(= , = )

 

Examples:

 

EXAMPLE 1

Given : =

Prove : =

Statements

Reasons

1.

1. Given

2. PQ = XY

2. Definition of congruent segment

3. XY = PQ

3. Symmetric property of equality

4.

4. Definition of congruent segements

 

Paragraph Proof: You are given that . By the definition of congruent segments, PQ = XY. By the symmetric property of equality, XY = PQ . Therefore, by the definition of congruent segments, if follows that .

 

EXAMPLE 2

 

 

More Examples on the Symmetric Property:

1)

Given: XY= 8, XZ=8, and the length of XY is congruent to the length of ZY(could not write it)

 

Prove: the length of XZ is congruent to the length of ZY

 

 



        Statement                                                        Reasoning                                              

 

XY=8, XZ=8                                                             Given 

X=XY 

XY=XZ                                                                   Transitive Property of Equality 

The length of XY is congruent to the length of XZ     Definition of Congruent Segments 

The length of XY is congruent to the length of ZY     Given 

The length of XZ is congruent to the length of ZY     Transitive Property of Segment Congruency

 

 

 

2)

 

Given: The length of VW is congruent to the length of WX, The length of WX is contruent to the length of YZ

 

Prove: The length of UW is congruent to the length of XZ

 

        Statement                                                        Reasoning                                              

 

The Length of UV is congruent to the length of XY,          

 The length of VW is congruent to the length of WX,          Given 

The length of WX is congruent to the length of YZ

 

 THe length of VW is congruent to the length of YZ           Definition of congruent segments

 UV=XY, VW=YZ                                                             Definition of congruent segments 

UV+VW=XY+YZ                                                             Segment Addition Postulate

 UV+VW=UW, XY+YZ= XZ                                               Addition property of equality 

UW=XZ                                                                         Substitution property of equality

 The length of UW is congruent to the length of XZ           Transitive Property of Segment Congruence

 

 

3)

 

Given: The length of AB is congruent to the length of JK, the length of JK is congruent to the length of ST

 

Prove: THe length of AB is congruent to the length of ST

 

        Statement                                                        Reasoning                                              

 

The length of AB is congruent to the length of JK,                Given 

The length of JK is congruent to the length of ST 

AB = JK, JK =ST                                                                 Definition of Congruent Segments 

AB = ST                                                                            Transitive property of equality 

The length of AB is congruent to the length of ST                 Definition of congruent segments 

 

 

4) Given:  VN is 10, LA is 10

 

    Prove : VN= LA

 

        Statement                                                        Reasoning                                              

VN is 10, LA is 10                                                      Given

VN= LA                                                                    Definition of equal segments 

  

  

      

Reflexive Property

For any segment, AB=AB. Meaning that the measurement of a segment equals its measurement, obviously . Until now, the reflexive property has been the least used in our class probibly because it is the most obvious of the properties. Really, there is no need to prove that A=A, we know it already, it isn't complicated(doesn't need explaining).

 

SOME EXAMPLES:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MORE EXAMPLES... 

1) 

EF = EF Given
EF ≡ EF
Definition of Congruent Segments

 

2) 

CD = CD Given
CD ≡ CD

 

Definition of Congruent Segments

 

3) 

DB = DB Given
DB ≡ DB
Definition of Congruent Segments

 

4)

ZT = ZT Given
ZT ≡ ZT
Definition of Congruent Segments

Transitive Property 

 

If a = b and b = c, then a = c

remember that if the points are in the same formula than this one the points all have the same degree. To prove the Transative property of Congruency for segment always begin by drawing the three congruent angles. And lebel them A,B,C or 1,2,3.

  

EXAMPLES...

 GIVEN... A congruent C, B congruent C

Statements

Reasons

1. A congruent B

B congruent to C

1. Given

2.  mA=mB

2. Definition of congruent segment

3. mB=mC

3. Definition of congruent segment

4. A=C

4. Transitive Property

 

 

 

5.  A congruent C

Definition of congruent segment

 

 



Statements

Reasons

1. <B congruent to <A

1. Given

2.  <A congruent to <E

2. Given

3. <B congruent to <E

3. Transitive Property

TTT!!!

 

 

 

 

Statements

Reasons

1. A congruent B

B congruent to D

1. Given

2.  <A congruent to <D

2. Transitive Property

3. (<C +<A + <B + <D)/4= <C

3. Division Property

TTT!!!

 

 

Statements

Reasons

1. <A congruent to <C

<A+<C=<B

1. Given

2.  <B=90 degrees

2. Def of Right angle

3. <D=180 degrees

3. def of Straight angle

4. <A+<B+<C=<D

4. Transitive

 

5. <A+<A=<B 

Substitution

6. 2<A=<B

6. Multiplication

7. 2<A=90 degrees

7. Substitution

3. <A=45 degrees

3. Division Property

TTT!!!

 

 



Statements

Reasons

1. AB congruent JK, JK congruent ST

1. Given

2.  AB=JK, JK=ST

2. Definition of congruent segment

3. AB=ST

3. Transative property

4. AB congruent ST

4. Definition of congruent segment

 

Statements

Reasons

1.<B+<C=180 degrees

1. Supplementary

2.  <B congruent to <A

2. Given

3. <A congruent to <D

3. Given

4. <B congruent to <D

4. Transitive

 

 

Comments (2)

estuardoarriaga@... said

at 8:01 pm on May 12, 2010

qn esta trabajando aorita

Katia Castillo said

at 10:29 pm on May 12, 2010

woo hoo!! terminamos :)

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