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Overlapping Triangle Proofs

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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