What can you assume if.. (triangles)?

Question

Given: If a triangle has two congruent sides, then the angles opposite those sides are congruent.

What can you assume if, in triangle DEF, the measure of angle D is not equal to the measure of angle F?

Also, for the same given statement, what can you assume if, in triangle LMN, the measure of angle L is equal to the measure of angle M? Explanations are much appreciated, thanks!

Answer 1

You can assume that angle E is either congruent to angle D or angle F.

Answer 2

Assuming that triangle DEF is the one with two congruent sides, then either angle D or angle F is equal to angle E. Also, sides DE (opposite angle F) and EF (opposite angle D) are not congruent, but one of them is congruent with side DF (opposite angle E).

For your second triangle LMN : if L = M, then sides LN (opposite angle M) and MN (opposite angle L) are congruent.

Answer 3

Not sure from your problem if triangle DEF is congruent. If it is congruent, then two sides are of the same length and the two sides which are the same length are the sides opposite equal angles (congruent angles).
Since you are told that angle D is not equal angle F, then either angle E must equal angle D or angle E must equal angle F.
If angle E = angle D, then side DF must equal the length of side EF
If angle E = angle F, then DE must equal DF.

Answer 4

Best way to check is not to assume - but to actually draw your doubts on a piece of paper in the form of a triangle

Answer 5

side DE not equal to side EF.