Triangle Proofs Practice

What is the "reason" for step 5 of the proof?

• Angle Bisector Theorem

• Reflexive property

• CPCTC Theorem

• Proof

Fill in the Reason.

• Opposite sides of a parallelogram are congruent.

• definition of parallelogram

• Prove

• CPCTC

What is the reason?

• Definition of Complementary

• Definition of 180 

• Definition of supplementary

• Angle Addition

Name the property of equality or congruence that justifies going from the first statement to the second statement.

• Reflexive Property of Congruence

• Symmetric Property of Congruence

• Distributive Property

• Transitive Property of Congruence

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

Statements Reasons

• ∠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

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

∠SEM

SAS congruence postulate

RM ≅ EM

Definition of midpoint

AAS congruence theorem

△SEM ≅ △KMR

Alternate internal ∠’s are ≅

CPCTC

∠SMR

SM

Given: \overline{PQ}\cong\overline{ST},\ \angle PQS\cong\angle RSQ Prove: \Delta PQS\cong\Delta RSQ

• Given

• Reflexive Property

• SAS Congruence Postulate

• SSA Congruence Postulate

• SSS Congruence Postulate

• Symmetric Property

• Alternate Interior Angle Thm.