Question

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.

Answer 1

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

Answer 2

The theorem is: B. AAS Congruence Theorem.

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

• The image shows Quadrilateral FGHJ. From the image, we can deduce the following:

There are two triangles, $\triangle FGJ and \triangle HJG$

• Thus:

$\angle F = \angle H$ (congruent angles given)

$\angle FGJ = \angle HJG$ (congruent angles given)

$\overline {JG}$ is a side shared by $\triangle FGJ and \triangle HJG$,

Therefore, $\overline {JG} = \overline {JG}$

• From what have been stated above, it implies that:

Two angles and one non-included side in $\triangle FGJ$ are congruent to two corresponding angles and a corresponding non-included side in $\triangle HJG$.

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:

B. AAS Congruence Theorem.

Learn more about AAS Congruence Theorem here:

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