Which postulate or theorem proves that these two triangles are congruent? sas congruence postulate aas congruence theorem hl congruence theorem asa congruence postulatequadrilateral f g h j with a line segment connecting vertices j and g. angles f and h are each labeled with 1 arc. angles f g j and h j g are each labeled with 2 arcs.

The information given has been sketched out in the image attached below.

There are two triangles,

(congruent angles given)

(congruent angles given)

is a side shared by ,

Therefore,

Two angles and one non-included side in are congruent to two corresponding angles and a corresponding non-included side in .

This satisfies the Angle-Angle-Side Congruence Theorem(AAS) that states that two triangles are congruent to each other if they have two corresponding angles and one corresponding non-included side that are congruent in each of the triangles.

Therefore, the theorem that proves that both triangles are equal is:

Learn more about AAS Congruence Theorem here:

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ANSWER

Two triangles are congruent by the  AAS Congruence Theorem

Reason

AAS congurence property

In this property two angles and one side of two triangles are equal.

diagram is shown below

In the quadilateral FGHL their exit two triangle .

in the  ΔFGJ and ΔGHJ .

∠GFJ = ∠GHJ  ( As given )

∠FGJ = ∠GJH ( As given )

JG = JG ( Common )

ΔFGJ ≅ ΔGHJ

by using the AAS congurence property .

Hence proved