Proofs of Triangle Congruences

Definition of congruence

Reflexive Property of Congruence

Segment Addition Postulate

Definition of Midpoint

$$\overline{JK}\cong\overline{JK}$$ ; Reflexive

$$\angle M\cong\angle L$$ ; Reflexive

$$\overline{MJ}\cong\overline{LK}$$ ; Midpoint Theorem

$$\overline{MK}\cong\overline{LJ}$$ ; Hypotenuse Congruence

$$\angle P\cong\angle Q$$ ; SAS

$$\angle P\cong\angle Q$$ ; CPCTC

$$\angle P\cong\angle Q$$ ; SSS

$$\angle P\cong\angle Q$$ ; SSA

$$\overline{DC}\cong\overline{DC}$$ ; Reflexive Property

$$\angle A\cong\angle B$$ ; Reflexive Property

$$\angle1\cong\angle2$$ ; Reflexive Property

$$\overline{AD}\cong\overline{DB}$$ ; Midpoint Theorem

$$\overline{WE}\cong\overline{QE}$$ ; Midpoint Theorem

$$\overline{WN}\cong\overline{GQ}$$ ; Prove

$$\angle W\cong\angle Q$$ ; Alternate Interior

$$\angle N\cong\angle G$$ ; Alternate Interior

$$\angle APB\cong\angle CPD$$ ; Vertical

$$\angle A\approx\angle D$$ ; Alternate Interior

$$\angle C\cong\angle B$$ ; Alternate Interior

$$\overline{AB}\cong\overline{CD}$$ ; Prove

$$\overline{TM}\cong\overline{ME}$$ ; Midpoint Theorem

$$\overline{IM}\cong\overline{MR}$$ ; Midpoint Theorem

$$\angle I\cong\angle R$$ ; Alternate Interior

$$\overline{MI}\cong\overline{MR}$$ ; Prove

of the ASA Triangle congruence postulate.

of the SSA Triangle congruence theorem.

of the SSS Triangle congruence postulate.

of the HL Triangle congruence postulate.

of the AAS Triangle congruence theorem.

of the SAS Triangle congruence theorem.

there is not enough information given.

congruent

not congruent

EO ≅ TE

∠YTE ≅ ∠YES

∠ESO ≅ ∠TES

GM ≅ MK

GR ≅ GR

OT ≅ ZE

∠OMS ≅ ∠MSE