Question

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

Answer 1

Answer:

a) yes, by AA criterion

Step-by-step explanation:

If two angles in a triangle are congruent to two angles in another triangle then the two triangles are congruent. ∠ABE ≈ ∠EDC since they have the same measure. ∠BEA ≈ ∠CED since they are vertical angles. Since two angles are congruent, then you can conclude yes, by AA criterion

Answer 2

Answer:

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.