Determine whether the two triangles can be proven congruent using the ASA congruence method. If so, select the congruence statement.
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The correct congruence statement is ΔEFG ≅ ΔHFG.

We have to determine, Whether the two triangles can be proven congruent using the ASA. select the correct statement.

Congruence method; If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and sides included between the angles of the second triangle.

Then, the two triangles are said to be congruent by the ASA rule.

Then, whether the two triangles can be proven congruent using the ASA.

From the given figure attached In ΔEFG and ΔHFG,

By the congruence method, the correct statements are,              

1). ∠EFG ≅ ∠HFG  

2). ∠EGF ≅ ∠HGF                  

3). Side FG ≅ side FG            

4). ΔEFG ≅ ΔHFG                  

Therefore, The correct congruence statement is ΔEFG ≅ ΔHFG.

To know more about the Congruence Method click the link given below.

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Option (B).

Step-by-step explanation:

From the figure attached,

In ΔEFG and ΔHFG,

           Statements                    Reasons

1). ∠EFG ≅ ∠HFG                   1). Given

2). ∠EGF ≅ ∠HGF                  2). Given

3). Side FG ≅ side FG           3). Reflexive property

4). ΔEFG ≅ ΔHFG                  4). By ASA property of congruence

Therefore, ΔEFG ≅ ΔHFG  

Option (B) will be the answer.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

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step-by-step explanation: