Geometry Triangle Proofs

Since segment BD is part of both triangles, it is congruent to itself, what do we call this?

• Substitution Property

• Commutative Property

• Reflexive Property

• CPCTC

• Reflective Property

What is statement #1?

• BC≅DC

• AC≅EC

• BC≅DC, AC≅EC

• ∆BCA≅∆DCE

What is statement #2?

• ∠ABC≅∠EDC

• ∠BCA≅∠DCE

• BC≅CD

• ∠E≅∠A

Can the HL Congruence Theorem be used to prove the triangles congruent? If so, write a congruence statement.

• Yes, △ABC≅△YXW

• Yes, △CBA≅△WXY

• Yes, △BCA≅△XYW

• No

What is the "statement" for step 3 of the proof? 

• ∡EDA≅∡DCB

• ∡AED≅∡BEC

• DE=CE

• ∡AED≅∡CED

Statements Reasons

1. ​ (a)   1. Given

2. ​ (b)   2. Given

3. ​ (c)   3. Given

4. ​ (d)   4. Definition of midpoint

5. ​ (e)   5. AAS

• ∠DBM ≅ ∠FCM

• ∠BDM ≅ ∠CFM

• M is the midpoint of DF

• DM ≅ MF

• △BDM ≅ △CFM

• ∠BMD ≅ ∠CMF

• BM ≅ CM

• BD ≅ CF

• Definition of midpoint

• Definition of bisect

Statements Reasons

1. ∠A ≅ ∠C 1. ​ (a)  

2. BD bisects ∠ABC 2. ​ (b)  

3. ∠DBA ≅ ∠DBC 3. ​ (c)  

4. BD ≅ BD 4. ​ (d)  

5. △ABD ≅ △CBD 5. ​ (e)  

• Given

• Definition of bisect

• Reflexive

• AAS

• Definition of midpoint

• SSS

• SAS

• ASA

• Vertical Angles Theorem

• Linear Pairs Theorem

• Corresponding Angle Postulate

• Midpoint Thm.

• SAS Congruence Postulate

• AAS Congruence Postulate

• Alt Int Angle Thm.

• SSA Congruence Postulate

Statements Reasons

• ∠1 ≅ ∠2

• JG bisects EH at F

• EF ≅ FH

• ∠3 ≅ ∠4

• △EFJ ≅ △HFG

• ∠EJF ≅ ∠HGF

• EJ ≅ GH

• JF ≅ FG

• Definition of bisect

• Definition of midpoint

Fill in the proof with the labels below.

f

g

h

b

c

e

i

a

d

j

SAS congruence postulate

Alternate internal ∠’s are ≅

AAS congruence theorem

SM

△SEM ≅ △KMR

∠SMR

∠SEM

CPCTC

Definition of midpoint

RM ≅ EM