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# Segment proofs

last edited by 11 years, 2 months ago

# 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=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. Statements Reasons 1. A congruent B B congruent to D 1. Given 2. Statements Reasons 1.
 5.
﻿
 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. #### 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 :)