1Geometry Lesson: Pairs of Triangles in Proofs

Aim: How do we use two pairs of congruent triangles in proofs?

Do Now:

A

D

RL B

P

KM1) Given that , what can be said about:

a) and ? b) and ?2) What additional information do we need to prove using S.A.S or A.S.A. ?

DAR PBK

DR PKR K

DLR PMK

DR PKR K

2Geometry Lesson: Pairs of Triangles in Proofs

Proofs using pairs of triangles:1) Prove one pair of triangles congruent using the given

information.2) Use CPCTC and extra Given’s to prove that another

set of triangles is congruent.

A

D

RL B

P

KM

Ex: GivenDAR PBK LR MKProve: DLR PMK

, DR PK R K DAR PBK Given

CPCTCLR MK GivenDLR PMK S.A.S. Postulate

3Geometry Lesson: Pairs of Triangles in Proofs

Proofs w/ pairs of triangles

D

X T G

Q

S V F

3) Given:

Prove:

DXG QXF bisects DT XDG , bisects QV SQF

,DXT QXV DT QV

L

B

PF

GE

R2) Given:

Prove:

, ,BPL RPG EPF, BP PL RP PG

,BPE LFP E F

R

F

Q

A

P1) Given:

Prove:

RQ FA , FRP ARP

FQP AQP

4Geometry Lesson: Pairs of Triangles in Proofs

Proofs w/ pairs of triangles

R

F

Q

A

P4) Given:

Prove:

, RF RA FQ AQ intersects at RQ FA P

FPQ APQ

T J

N

E

Q

5) Given:

Prove:

, NQ NJ EQ EJ

, NQT NJT QT JT

5Geometry Lesson: Pairs of Triangles in Proofs

Solution #3

Statements Reasons1) 1)2) 2)3) 3)

4) 4)5) 5)

6) 6)

7) 7)8) 8)9) 9)

Given

GivenDef. angle bisector

C.P.C.T.CXDG SQF C.P.C.T.C

Substitution Post.

bisects , bisects DT XDG QV SQF

DX QS , X S

1 1,2 2

m XDT m XDG m SQV m SQF

1 1,2 2

m XDT m XDG m SQV m XDG

Transitive Post.DXT QXV A.S.A. Post.DT QV C.P.C.T.C

XDT SQV

D

X T G

Q

S V F

DXG QSF

6Geometry Lesson: Pairs of Triangles in Proofs

Solution #5

Statements Reasons1) 1)2) 2)3) 3)

4) 4)5) 5)

6) 6)

7) 7)

Given

N

T JE

Q

, NQ NJ EQ EJ NE NE Reflexive PostulateNQE NJE S.S.S. PostulateQNE JNE C.P.C.T.C

NT NTNQT NJT S.A.S. Postulate

Reflexive Postulate

QT JT C.P.C.T.C

Given:

Prove:

, NQ NJ EQ EJ

, NQT NJT QT JT