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

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

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