If ∠ABE = 100° and ∠EDC = 100°, are the two triangles, ΔABE and ΔEDC similar? If so, by what criterion?

A) yes, by AA criterion

B) yes, by SAS criterion

C) yes, by SSA criterion

D) no, not possible to tell.

No, not possible to tell that  the two triangles, ΔABE and ΔEDC are similar

Step-by-step explanation:

Similarity criterion:

1. AAA similarity : two triangles are similar if all three angles in the first

 triangle equal the corresponding angle in the second triangle  

2. AA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.

3. SSS similarity : If the corresponding sides of the two triangles are

proportional, then the two triangles are similar.

4. SAS similarity : In two triangles, if two sets of corresponding sides  

are proportional and the included angles are equal then the two  

triangles are similar.

Now in the two triangles ABE and EDC :

∠ABE = 100°

∠EDC = 100°

∠ABE =  ∠EDC

But only one congruent angle  does not  not prove that the two triangles are similar.

Hence, NOTHING CAN BE SAID ABOUT THE nature of the triangle.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!