Question

In \[\Delta ABC\] and \[\Delta DEF\],\[AB = FD\] and \[\angle A = \angle D\]. The two triangle will be congruent by SAS axioms, if

A) \[BC = EF\]
B) \[AC = DE\]
C) \[AC = EF\]
D) \[BC = DE\]

Answer 1

Hint: As per the SAS axioms, if the triangle is congruent then by the stated axioms it’s two sides and one angle will be equal. So, first, we draw the triangle and observe the given data of the triangle given above and hence choose the correct option.

Remember a side, it’s the corresponding angle, and its adjacent side will be equal and hence the congruency of the triangle is stated.

Complete step by step solution: As the given are \[\Delta ABC\] and \[\Delta DEF\],\[AB = FD\] and \[\angle A = \angle D\]. So, draw the diagram as per the given.

Hence, we can see that \[\angle A = \angle D\]and also the side \[AB = FD\].

Hence, using SAS axioms aside, it’s the corresponding angle, and its adjacent side will be required for two triangles to be congruent

Hence in triangle ABC, we see that angle A lies between side AB and AC, similarly in triangle DEF angle D lies between Sides DF and DE

Hence from SAS axiom we have,\[AC = DE\] .

Thus, option (B) is our correct answer.

Note: Note: ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.

SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.