Triangle Proofs Practice

Angle Bisector Theorem

Reflexive property

CPCTC Theorem

Proof

Opposite sides of a parallelogram are congruent.

definition of parallelogram

Prove

CPCTC

Definition of Complementary

Definition of 180 

Definition of supplementary

Angle Addition

Reflexive Property of Congruence

Symmetric Property of Congruence

Distributive Property

Transitive Property of Congruence

∠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

∠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

Given

Definition of bisect

Reflexive

AAS

Definition of midpoint

SSS

SAS

ASA

Vertical Angles Theorem

Linear Pairs Theorem

∠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

Given

$$\overline{QS}\cong\overline{QS}$$  

Reflexive Property

$$\Delta PQS\cong\Delta RSQ$$  

SAS Congruence Postulate

$$\angle P\cong\angle R$$  

SSA Congruence Postulate

SSS Congruence Postulate

Symmetric Property

Alternate Interior Angle Thm.