Question

If AB = DE CA = FD angle B is congruent to angle E angle A is congruent to angle D , then ∆ABC and ∆DEF are congruent by the ASA criterion.

Answer 1

True

Explanation:

It is given that from ∆ABC and ∆DEF,

∠B=∠E (given)

AB=DE (given)

∠A=∠D( given)

Therefore, by ASA rule,

∆ABC≅∆DEF.

Thus, ∆ABC and ∆DEF are congruent by the ASA criterion which is true.

Also, from ∆ABC and ∆DEF

AB=DE(given)

∠A=∠D(given)

AC=DF(given)

Hence by SAS rule,

∆ABC≅∆DEF.

Thus, ∆ABC and ∆DEF are congruent by the SAS criterion which is also true.

Answer 2

1) the SAS criterion
Two triangles are congruent if they have two sides and the angle determined by them respectively equal.
AB = DE CA = FD (two sides equal)
angle B is congruent to angle E angle A is congruent to angle D (angle determined by the two sides respectively equal)
by the SAS criterion ∆ABC and ∆DEF are congruent

2) the ASA criterion
Two triangles are congruent if they have two angles and the side common to them, respectively, equal.
angle B is congruent to angle E angle A is congruent to angle D (two angles equal)
AB = DE (the side common to the angles is equal)
by the ASA criterion ∆ABC and ∆DEF are congruent

The answer is ∆ABC and ∆DEF are congruent by the SAS criterion and by the ASA criterion