Question

If ZABE = 100° and ZEDC = 100°, are the two triangles, AABE and AEDC similar? If so, by what criterion?
yes, by AA criterion
yes, by SAS criterion
yes, by SSA criterion
no, not possible to tell

Answer 1

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.

In the two triangles ABE and EDC :

m∠ABE = 100°

m∠EDC = 100°

m∠ABE = m∠EDC

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