Question

In the given figure , apply SSS congruence and state the result in the symbolic from.
     

Answer 1

Hint: When two triangles are congruent, they will have exactly the same three sides and exactly the same three angles. The equal side and angle may not be in the same position (if there is turn or flip), but they are there.
There are four ways to find if the triangles are congruent: SSS, SAS , ASA and HL.
SSS- (side, side, side)
ASA- (angle, side, angle)
SAS- (side, angle, side)
HL- (hypotenuse, leg)
In this question clearly mention that you have two use SSS to prove that the two triangle are congruent
Because we have only sides in this question.
So we need three sides which are equal to the other three sides of the second triangle.

Complete step-by-step answer:
In triangle $\vartriangle ABD$ $and$ $\vartriangle ACD$
Side AB = side AC = 4
Side BD = side CD = 3
Side AD = side AD = 7 …………… common
Here we have sides of triangle ABD equal to corresponding sides of triangle ACD
Hence prove that
$\vartriangle ABD \cong \vartriangle ACD$
Triangle ABD is congruent to triangle ACD

Note: Those questions which are related to proving congruence try to look and simplify the diagram first. here the important part is two triangles are said to be congruent if all their three sides and three angles are equal. Always remember the ways of proving triangles congruent which are SSS, SAS, ASA and RHS(HL). Find the equal parts in both triangles whether they are angles or sides and in most cases there is always a common side in both triangles.