Question

In and, AB=DF and $\angle A$=$\angle D$. The two triangles will be congruent by SAS axiom if:
A) BC=EF
B) AC=DE
C) BC=DE
D) AC=EC

Answer 1

Hint: Here we can apply the SAS congruent property of triangle which states that if two sides and included angle between them of one triangle is equal to corresponding two sides and there included angle between them of another triangle then triangles are said to be congruent.

Complete step by step solution:
With the help of a figure we will do this question which is given below.

In ABC and DEF you can see that two conditions are given: one is of side and other is of angle so we require one more side so that triangles can be congruent.
AB=DE (Given)
$\angle A = \angle D$ (Given)
AC=DE(To make two triangles congruent we required these sides to be equal because only these sides are including the angles given)
Answer will be AC=DE
So, two triangles will be $ \cong $ by Side angle side axiom (SAS)

Therefore option (B) is the correct answer.

Note:
When you are applying the property make sure you should take the right sides and angles otherwise the whole property can change its meaning. Sides should only be valid if they are adjacent to angle.
There are more congruent properties of a triangle:-
SSS (side side side) congruency – It states that when all the sides of one triangle is equal to the corresponding sides of the another triangle then it is said to be SSS property of congruency.
ASA (angle side angle) congruency – It states that if two angles including side of one triangle are equal to corresponding two angles and including side of another triangle then it is said to be ASA congruency.