Triangle Congruency - CPCTC

Mixed Problems

Corresponding Parts of Congruent Triangles are Congruent

This rule is used AFTER we have proven two triangles congruent!

We need to be able to determine what corresponding parts are, so lets figure it out…

Statement Reason

1. Given

2. Given

Pg. 8 #7

CBCA 1.

BDCADC ΔΔ .4 SSSSSS .4

CDCD .3 3. Reflexive postulate

BDAD 2.

Part B: Three pairs of congruent angles

BA 1.BDCADC 2.BCDACD 3.

Statement Reason

1. Given

2. Given

Pg. 8 #8

ABAD 1.

ABCADC ΔΔ .4 SASSAS .4

ACAC .3 3. Reflexive postulate

21 2.

Part B: Three more congruent parts

DB 1.BCADCA 2.

BCCD 3.

Statement Reason

1. Given

2. Given

Pg. 8 #9

ABCBD bisects 1.

CBDABD ΔΔ .5 ASAASA .5

43 21 .3

3. An angle bisector divides an

angle into two congruent parts

Part B: Three more congruent parts

CA 1.

CDAD 2.

BCAB 3.

ADCDB bisects 2.

BDBD .4 4. Reflexive postulate

Statement Reason

1. Given

2. Segment bisectors divide a segment into two congruent parts

Pg. 8 #10

ECDAB

at other each bisect and 1.

BEDAEC ΔΔ .4 SASSAS .4

21 .3 3. Vertical angles are congruent

EBAEEDCE

2.

DC .5 5. Corresponding parts of congruent triangles are congruent

Statement Reason

1. Given

2. Given

Pg. 8 #11

CDAB 1.

CBAADC ΔΔ .4 SSSSSS .4

ACAC .3 3. Reflexive postulate

DABC 2.

DB .5 5. Corresponding parts of congruent triangles are congruent

Statement Reason

1. Given

2. Given

Pg. 8 #12

21 1.

CBAADC ΔΔ .4 ASAASA .4

ACAC .3 3. Reflexive postulate

43 2.

BADC .5 5. Corresponding parts of congruent triangles are congruent

Statement Reason

1. Given

2. Given

Pg. 8 #13

21 1.

BDCADC ΔΔ .8 SASSAS .8 CDCD .7 7. Reflexive postulate

CFCE 2.

43 .9 9. Corresponding parts of congruent triangles are congruent

3. GivenFBEA 3.

FBCFEACE .4 4. Addition Postulate

5. Partition Postulate

BCCA 6. 6. Substitution Postulate

BCFCBFCAEACE

.5

8. Corresponding parts of congruent triangles are congruent

Statement Reason

1. Given

2. Given

Pg. 9 #15

RTSTQ bisects 1.

STQRTQ .3 3. An angle bisector divides an angle into two congruent parts

RSTQ 2.

TQTQ .6 6. Reflexive postulate

anglesright are and .4 TQSTQR 4. Perpendicular segments

form right angles

5. All right angles are congruentTQSTQR 5.

SQTRQT .7 ASAASA .7 QSRQ .8

.

Statement Reason

1. Given

2. Given

Pg. 9 #16

DEDC 1.

ADEADC ΔΔ .8 SASSAS .8 ADAD .7 7. Reflexive postulate

yx 2.

ACAE .9 9. Corresponding parts of congruent triangles are congruent

3. Givenwz 3.

wyzx .4 4. Addition Postulate

5. Partition Postulate

6. Substitution Postulate

EDAwyCDAzx

.5

EDACDA .6

Statement Reason

AEAD 2. 2. Given

Pg. 9 #17

anglesright are and 5. FABCAB

FABCAB 6.

5. Perpendicular segments form right angles

CFAB

ofbisector lar perpendicu theis 1. 1. Given

FAECAD ΔΔ .10 SASSAS .10

AFCA 4. 4. A segment bisector divides a segment into 2 congruent parts

21 3. 3. Given

6. All right angles are congruent

21 .7 FABCAB 7. Subtraction Postulate

8. Partition Postulate

FAECAD 9. 9. Substitution Postulate

FAEFABCADCAB

2 1 .8

ED .11 11. Corresponding parts of congruent triangles are congruent

Statement Reason

1. Given

2. Given

Pg. 9 #18

GHF ofmidpoint theis 1.

HFBGFC ΔΔ .8 SASSAS .8 21 .7 7. Vertical angles are congruent

EDFC 3.

HBGC .9 9. Corresponding parts of congruent triangles are congruent

3. Given

AEBF 4.

6. Substitution Postulate

ADE ofmidpoint theis 2.

4. Given

5.EDAEFHGF

5. A midpoint divides a segment

into 2 congruent parts

FCBF 6.

1

2

Statement Reason

1. Given

2. Given

Pg. 9 #21

CBAD 1.

CBDADB ΔΔ .4 SASSAS .4

DBDB .3 3. Reflexive postulate

21 2.

CDAB .5 5. Corresponding parts of congruent triangles are congruent