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Using Congruent Triangles. Ch 4 Lesson 5. CPCTC. Corresponding parts of congruent triangles are congruent (CPCTC): Once two triangles are proven to be congruent than all corresponding parts of the two triangles are congruent. Example #1. Given AB II CD, BC II DA Prove AB ≅ CD - PowerPoint PPT Presentation
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Using Congruent Triangles
Ch 4
Lesson 5
CPCTC
• Corresponding parts of congruent triangles are congruent (CPCTC): Once two triangles are proven to be congruent than all corresponding parts of the two triangles are congruent
Example #1
• Given AB II CD, BC II DA
• Prove AB CD≅• Copy the diagram with signs to show
parallel sides
Example #1: Prove AB CD≅
Statement
AB II CD
BC II DA
<1 <4≅<2 <3≅BD BD≅ABC BDC≅AB CD≅
Reason
Given
Given
Alternating Angles
Alternating Angles
Reflexive prop.
Def of triangles (ASA)≅Corresponding Sides of
congruent triangles are congruent
Example #1: Prove AB CD≅
Statement
AB II CD
BC II DA
<1 <4≅<2 <3≅BD BD≅ABC BDC≅AB CD≅
Reason
Given
Given
Alternating Angles
Alternating Angles
Reflexive prop.
Def of triangles (ASA)≅Corresponding Sides of
congruent triangles are congruent
Example #1: Prove AB CD≅
Statement
AB II CD
BC II DA
<1 <4≅<2 <3≅BD BD≅ABC BDC≅AB CD≅
Reason
Given
Given
Alternating Angles
Alternating Angles
Reflexive prop.
Def of triangles (ASA)≅Corresponding Sides of
congruent triangles are congruent
Example #1: Prove AB CD≅
Statement
AB II CD
BC II DA
<1 <4≅<2 <3≅BD BD≅ABC BDC≅AB CD≅
Reason
Given
Given
Alternating Angles
Alternating Angles
Reflexive prop.
Def of triangles (ASA)≅Corresponding Sides of
congruent triangles are congruent
Example #1: Prove AB CD≅
Statement
AB II CD
BC II DA
<1 <4≅<2 <3≅BD BD≅ABC BDC≅AB CD≅
Reason
Given
Given
Alternating Angles
Alternating Angles
Reflexive prop.
Def of triangles (ASA)≅Corresponding Sides of
congruent triangles are congruent
Example #1: Prove AB CD≅
Statement
AB II CD
BC II DA
<1 <4≅<2 <3≅BD BD≅ΔABC ΔBDC≅AB CD≅
Reason
Given
Given
Alternating Angles
Alternating Angles
Reflexive prop.
Def of triangles (ASA)≅CPCTC
Example #1: Prove AB CD≅
Statement
AB II CD
BC II DA
<1 <4≅<2 <3≅BD BD≅ΔABC ΔBDC≅AB CD≅
Reason
Given
Given
Alternating Angles
Alternating Angles
Reflexive prop.
Def of triangles (ASA)≅CPCTC
Example #2
Given: A is midpoint of MT
A is midpoint of SR
Prove: MS II TR
Given: A is midpoint of MT A is midpoint of SR
Prove: MS II TRStatement
A is midpoint of MT
A is midpoint of SR
MA AT & SA AR≅ ≅<SAM <RAT≅Δ SAM Δ RAT≅<M <T & <S <R≅ ≅MS II TR
Reason
Given
Given
Def of ≅Vertical <s
SAS Theorem
CPCTC (alternating <s)
CPCTC (alternating <s)
Given: A is midpoint of MT A is midpoint of SR
Prove: MS II TRStatement
A is midpoint of MT
A is midpoint of SR
MA AT & SA AR≅ ≅<SAM <RAT≅Δ SAM Δ RAT≅<M <T & <S <R≅ ≅MS II TR
Reason
Given
Given
Def of ≅Vertical <s
SAS Theorem
CPCTC (alternating <s)
CPCTC (alternating <s)
Given: A is midpoint of MT A is midpoint of SR
Prove: MS II TRStatement
A is midpoint of MT
A is midpoint of SR
MA AT & SA AR≅ ≅<SAM <RAT≅Δ SAM Δ RAT≅<M <T & <S <R≅ ≅MS II TR
Reason
Given
Given
Def of ≅Vertical <s
SAS Theorem
CPCTC (alternating <s)
CPCTC (alternating <s)
Given: A is midpoint of MT A is midpoint of SR
Prove: MS II TRStatement
A is midpoint of MT
A is midpoint of SR
MA AT & SA AR≅ ≅<SAM <RAT≅Δ SAM Δ RAT≅<M <T & <S <R≅ ≅MS II TR
Reason
Given
Given
Def of ≅Vertical <s
SAS Theorem
CPCTC (alternating <s)
CPCTC (alternating <s)
Given: A is midpoint of MT A is midpoint of SR
Prove: MS II TRStatement
A is midpoint of MT
A is midpoint of SR
MA AT & SA AR≅ ≅<SAM <RAT≅Δ SAM Δ RAT≅<M <T & <S <R≅ ≅MS II TR
Reason
Given
Given
Def of ≅Vertical <s
SAS Theorem
CPCTC (alternating <s)
CPCTC (alternating <s)
Given: A is midpoint of MT A is midpoint of SR
Prove: MS II TRStatement
A is midpoint of MT
A is midpoint of SR
MA AT & SA AR≅ ≅<SAM <RAT≅Δ SAM Δ RAT≅<M <T & <S <R≅ ≅MS II TR
Reason
Given
Given
Def of ≅Vertical <s
SAS Theorem
CPCTC (alternating <s)
CPCTC (alternating <s)
Example #3
• Given: <1 <2 & <3 <4≅ ≅• Prove ΔBCE ΔDCE≅
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
Given: <1 <2 & <3 <4≅ ≅Prove: ΔBCE ΔDCE≅
Statement
<1 <2 & <3 <4≅ ≅CA CA≅ΔACD ΔABC≅CB CB≅In ΔDEC & ΔBEC
<1 <2≅CD CB≅CE CE≅ΔBCE ΔDCE≅
Reason
Given
Reflexive
ASA
CPCTC
Given
CPCTC
Reflexive
SAS
