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Overlapping Triangle Proofs. A. 2. If 2 sides of a triangle are congruent then the angles opposite the sides are congruent. ABC  ACB. D. E. BC  BC. Reflexive. BDC  CEB. SAS  SAS. B. C. BE  CD. CPCTC. Prove: BE  CD. D. C. ADC is right.

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Overlapping Triangle Proofs

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### Overlapping Triangle Proofs

A

2. If 2 sides of a triangle are congruent then the angles opposite the sides are congruent.

ABC  ACB

D

E

BC  BC

Reflexive

BDC  CEB

SAS  SAS

B

C

BE  CD

CPCTC

Prove: BE  CD

D

C

ADC is right

Perpendicular lines form right angles

BCD is right

ADC  BCD

All Right angles are congruent

A

B

CD  CD

Reflexive

Prove: AC = BD

SAS  SAS

ADC  BCD

CPCTC

AC  BD

D

If 2 lines are parallel, then alternate interior angles are congruent

A  C

C

DFC supplement to 1

BEA supplement to 2

Linear pairs are supplementary.

E

2

If 2 angles are congruent then their supplements are congruent

DFC  BEA

1

F

FE  FE

Reflexive

A

AF + FE  CE + FE

AE CF

Addition

B

ABE  DCF

ASA  ASA

Prove: ABE  DCF

Homework Problems

R

S

P

N

P is right

N is right

Perpendicular lines form right angles.

All Right angles are congruent

P  N

RS  RS

Reflexive

L

M

PR + RS = NS + RS

PS = NR

Addition

SAS  SAS

LPS  MNR

Prove: LPS  MNR

B

1  ½ BCA

2  ½ BAC

A bisector divides an angle into 2 congruent angles.

D

E

1  2

Division

2

1

AC  AC

Reflexive

A

C

ADC  CEA

ASA  ASA

Prove: ADC  CEA

B

3

Reflexive

AC  AC

D

E

DCA  EAC

SSS  SSS

DCA  EAC

CPCTC

A

C

Prove: DCA  EAC

C

4.

1

2

Reflexive

DE  DE

AE - DE  BD - DE

AD  BE

Subtraction

D

B

A

E

ACD  BCE

SSS  SSS

Prove: 1  2

1  2

CPCTC