Statement Reason

E G

HF

Given

Given

Alt. Int. <s Thm.

Reflex. Prop of

p.244ex4

SAS. Steps 1,3,4

Statement Reason

J

K L

M

p.246ex4

Given

Given

Reflex. Prop of ≅

<JKL≅<MLK

SAS Steps 1,2,3

Statement Reason

p.244 ex 4

A

B C

D

Given

Alt. Int. <s Thm.

Given

SAS Steps 3,2,4

Reflexive Prop of ≅

Statement Reason

Given: <ZVY≅<WYV, <ZVW≅<WYZ,VW≅YZ

Prove:

V

Y

X

W

Z

p.247: 21

Given

Def. of ≅

m<WVY = m<ZYV

Def. of ≅

Given

SAS, Steps 6,5,7

<ZVY≅<WYV, <ZVW≅<WYZ

m <ZVY = m <WYV,m <ZVW = m <WYZ

m <ZVY + m <ZVW = m <WYV + m <WYZ

<WVY≅ <ZYV

Reflex. Prop of ≅

<Add. Prop of =

<Add. Post

Determine if you can use ASA to prove the triangles congruent. Explain.

No, no included side

p. 246:13

Given: B is the midpoint of

A

B CD

B is the mdpt of DC

Given

Given

Def. Mdpt.

SAS Steps2,4,5

Reflex. Propof ≅

<ABD and <ABC areright <s

<ABD≅<ABC

Statement Reason

Statement Reason

Determine if you can use ASA to prove ΔUVX≅ΔWVX. Explain. p.253ex2X

UV

W

<WVX is a right angle

<UXV ≅ <WXV

given

given

Reflex. Prop

Def. of LinearPair

<WVX ≅ <UVX

1000

Given:

What is the measure of y?

y

l

m

Determine if you can use ASA to prove ΔNKL≅ΔLMN. Explain.

p.253ex2

KL

MN

By Alt. Int. <s Thm,

<KLN≅<MNL

Reflex. Prop

No other congruence relationships can be determined, so ASA cannot be applied.

Determine is you can use the HL Congruence Theorem to prove the triangles congruent.If not, tell what else you need to know.

p.255ex4

Yes No, need the hyp ≅

Yes

It is given that segment AC ≅ segment DB.

Seg. CB ≅ Seg. CB, by the Reflexive Prop.

Since <ABC and <DCB are rt <s, ΔABC and ΔDCB are rt triangles.

ΔABC≅ΔDCB by HL.

Statement Reason

Given: <G≅ <K, <J≅<M, HJ≅LMProve: ΔGHJ≅ΔKLM H

K

L

M

G J

p.254ex3

Given

Given

ASA Steps1,3,2

Third <s Thm

ΔGHJ ≅ ΔKLM

<H ≅ <L

<G ≅ <K, <J ≅ <M

Statement Reason

p.254ex3

Y

WZ VX

Use AAS to prove the triangles congruent.

Given: <X ≅ <V, <YZW ≅ <YWZ,

Prove: ΔXYZ≅ΔVYW

<X ≅ <V

<YZW ≅ <YWZ

AAS

Given

Given

Given

≅ Supps Thm

Def. of Supp <s

Def. of Supp <s

<XZY is suppto <YZW

<YWX is supp to <VWY

<YZX ≅ <YWV

≅XYZ ≅ ΔVYW

Statement Reason

AB

DE

F

C

Given:

Prove:

p. 257: 13

Given

Rt. < ≅Thm

GivenGiven

AAS

Statement Reason

p.257:15

Given: E is a midpoint of Segments AD and BCProve: Triangles ABE and DCE are congruent A

B

C

D

E

<A and <D are rt anglesGiven

E is mdpt ofSegs AD, BC

Given

HL

Rt. <s Thm

Def. of mdpt

Def. Rt Δs

Statement Reason

Given:

Prove:

p.258: 22

A B

E

CD

Given

Given

AAS

Vert. <s Thm

Alt. Int. <s Thm

Statement Reason

p. 258: 23

Given:

Prove: K

J

L

M

AAS

Given

GivenRt.<s Thm

Def. of Perpendicular

Statement Reason

p.259q4Given:

Prove:

A C

D

E

B

F G

ASA

Given

Given

≅ Supp Thm

Def. of Supp <s

<BAC is supp of <FAB;<DEC is suppof <GED

Statement Reason

Given:

Prove:E

FG

D

Use CPCTC

Given

Given

Alt. Int. <s Thm

Reflex. Prop of ≅

SAS

CPCTC

Converse of Alt. Int. <s Thm

Statement Reason

Given:

Prove:

p.261ex3b

Use CPCTC

N O

PM

Given

AAS

CPCTC

Alt. Int. <s Thm.

Reflex. Prop ≅

Conv. Alt. Int. <s Thm

Statement Reason

Given:

Prove:

Use CPCTC

A

B

C

D

Given

SSS

CPCTC

Def. of < Bisector

Reflex. Prop of ≅

Statement Reason

Given: M is the midpoint of

Prove:

Given

SAS

CPCTC

Vert <s Thm

Def. of mdpt

M

P

QR

S

Use CPCTC

p.263: 8

Statement Reason

p.263: 9Given:

Prove:

Use CPCTC

W X

YZ

Given

SSSCPCTC

Reflex. Prop ≅

Statement Reason

p.263: 10

Given:

Prove:

G is the midpoint of

G is the midpoint of

Given

Def. of mdpt Def. of ≅

Through any 2 pointsthere is exactly 1 line

Reflex. Prop of ≅

Given

SSS

CPCTC

≅ Supp. Thm

FG = HG

Draw

Use CPCTC

1 2

E

F G H

Statement Reason

p.263: 11Given:

Prove: M is the midpoint of

Given

Def. of < bisector Given

Reflex. Prop of ≅ SAS

CPCTC

Def. of mdpt

M is the midpoint of

L

MKJ

Use CPCTC

Statement Reason

Given: ΔQRS is adjacent to ΔQTS.

Prove:

ΔQRS is adjacent to ΔQTS.

Given

Def. of < bisect Reflex. Prop of ≅

AAS CPCTC

Def. of bisect

p.263:14

Statement Reason

Given: with E the midpoint of

Prove:

p.263: 15

Given

Def. of mdpt

Vert <s Thm

SAS

CPCTC

Conv. of Alt. Int. <s Thm

E is the mdpt. of

Use CPCTC

Given: PS = RQ, m<1 = m<4

Prove: m<3 = m<2

Given

Def. of Perpendicular

Def. of rt triangle

Given

Def. of ≅

Reflex. Prop of ≅

SAS

CPCTC

Def of ≅

PS = RQ

m<1 = m<4

m<3 = m <2

p.264:19

1

2

P

SR

Q3

4

Use CPCTC